[AY83] | I. A. A\izenberg and A. P. Yuzhakov, Integral representations and residues in multidimensional complex analysis, Translations of Mathematical Monographs, vol. 58, American Mathematical Society, Providence, RI, 1983, Translated from the Russian by H. H. McFaden, Translation edited by Lev J. Leifman. MR MR735793 (85a:32006) |
[AE04] | George E. Andrews and Kimmo Eriksson, Integer partitions, Cambridge University Press, Cambridge, 2004. MR MR2122332 (2006b:11125) |
[AGZV85] | V. I. Arnol'd, S. M. Guse\in-Zade, and A. N. Varchenko, Singularities of differentiable maps. Vol. I, Monographs in Mathematics, vol. 82, Birkhäuser Boston Inc., Boston, MA, 1985, The classification of critical points, caustics and wave fronts, Translated from the Russian by Ian Porteous and Mark Reynolds. MR MR777682 (86f:58018) |
[AGZV88] | , Singularities of differentiable maps. Vol. II, Monographs in Mathematics, vol. 83, Birkhäuser Boston Inc., Boston, MA, 1988, Monodromy and asymptotics of integrals, Translated from the Russian by Hugh Porteous, Translation revised by the authors and James Montaldi. MR MR966191 (89g:58024) |
[Bal00] | Werner Balser, Formal power series and linear systems of meromorphic ordinary differential equations, Universitext, Springer-Verlag, New York, 2000. MR MR1722871 (2001f:34169) |
[BBMD+02] | Cyril Banderier, Mireille Bousquet-Mélou, Alain Denise, Philippe Flajolet, Danièle Gardy, and Dominique Gouyou-Beauchamps, Generating functions for generating trees, Discrete Math. 246 (2002), no. 1-3, 29-55, Formal power series and algebraic combinatorics (Barcelona, 1999). MR MR1884885 (2003c:05008) |
[BFSS00] | Cyril Banderier, Philippe Flajolet, Gilles Schaeffer, and Michèle Soria, Planar maps and Airy phenomena, Automata, languages and programming (Geneva, 2000), Lecture Notes in Comput. Sci., vol. 1853, Springer, Berlin, 2000, pp. 388-402. MR MR1795907 (2001h:68113) |
[BFSS01] | , Random maps, coalescing saddles, singularity analysis, and Airy phenomena, Random Structures Algorithms 19 (2001), no. 3-4, 194-246, Analysis of algorithms (Krynica Morska, 2000). MR MR1871555 (2002k:05012) |
[BP] | Yuliy Baryshnikov and Robin Pemantle, Convolutions of inverse linear functions via multivariate residues, preprint available at http://www.math.upenn.edu/~pemantle/papers/Preprints/hyperplanes.pdf. |
[Ben73] | Edward A. Bender, Central and local limit theorems applied to asymptotic enumeration, J. Combinatorial Theory Ser. A 15 (1973), 91-111. MR MR0375433 (51 \#11626) |
[Ben74] | , Asymptotic methods in enumeration, SIAM Rev. 16 (1974), 485-515. MR MR0376369 (51 \#12545) |
[Ben76] | , Errata: “Asymptotic methods in enumeration” (SIAM Rev. 16 (1974), 485-515), SIAM Rev. 18 (1976), no. 2, 292. MR MR0437344 (55 \#10276) |
[BCM97] | Edward A. Bender, E. Rodney Canfield, and Brendan D. McKay, The asymptotic number of labeled graphs with n vertices, q edges, and no isolated vertices, J. Combin. Theory Ser. A 80 (1997), no. 1, 124-150. MR MR1472108 (98i:05098) |
[BLPW04] | Edward A. Bender, Gregory F. Lawler, Robin Pemantle, and Herbert S. Wilf, Irreducible compositions and the first return to the origin of a random walk, Sém. Lothar. Combin. 50 (2003/04), Art. B50h, 13 pp. (electronic). MR MR2118046 (2005m:60008) |
[BR83] | Edward A. Bender and L. Bruce Richmond, Central and local limit theorems applied to asymptotic enumeration. II. Multivariate generating functions, J. Combin. Theory Ser. A 34 (1983), no. 3, 255-265. MR MR700034 (85k:05009) |
[BR96] | , Admissible functions and asymptotics for labelled structures by number of components, Electron. J. Combin. 3 (1996), no. 1, Research Paper 34, approx.23 pp.(electronic). MR MR1418482 (98a:05012) |
[BR99] | , Multivariate asymptotics for products of large powers with applications to Lagrange inversion, Electron. J. Combin. 6 (1999), Research Paper 8, 21 pp. (electronic). MR MR1670294 (99j:41050) |
[BRW83] | Edward A. Bender, L. Bruce Richmond, and S. G. Williamson, Central and local limit theorems applied to asymptotic enumeration. III. Matrix recursions, J. Combin. Theory Ser. A 35 (1983), no. 3, 263-278. MR MR721368 (85k:05010) |
[BM93] | Andrea Bertozzi and James McKenna, Multidimensional residues, generating functions, and their application to queueing networks, SIAM Rev. 35 (1993), no. 2, 239-268. MR MR1220881 (95c:32005) |
[BH86] | Norman Bleistein and Richard A. Handelsman, Asymptotic expansions of integrals, second ed., Dover Publications Inc., New York, 1986. MR MR863284 (89d:41049) |
[BMP00] | Mireille Bousquet-Mélou and Marko Petkovšek, Linear recurrences with constant coefficients: the multivariate case, Discrete Math. 225 (2000), no. 1-3, 51-75, Formal power series and algebraic combinatorics (Toronto, ON, 1998). MR MR1798324 (2002a:05005) |
[BMS02] | Mireille Bousquet-Mélou and Gilles Schaeffer, Walks on the slit plane, Probab. Theory Related Fields 124 (2002), no. 3, 305-344. MR MR1939650 (2003h:60013) |
[BK86] | Egbert Brieskorn and Horst Knörrer, Plane algebraic curves, Birkhäuser Verlag, Basel, 1986, Translated from the German by John Stillwell. MR MR886476 (88a:14001) |
[Bri50] | Nelson A. Brigham, A general asymptotic formula for partition functions, Proc. Amer. Math. Soc. 1 (1950), 182-191. MR MR0034409 (11,582b) |
[CF69] | P. Cartier and D. Foata, Problèmes combinatoires de commutation et réarrangements, Lecture Notes in Mathematics, No. 85, Springer-Verlag, Berlin, 1969. MR MR0239978 (39 \#1332) |
[CGMO95] | Fan Chung, Ron Graham, John Morrison, and Andrew Odlyzko, Pebbling a chessboard, Amer. Math. Monthly 102 (1995), no. 2, 113-123. MR MR1315591 (95k:05015) |
[CMS05] | Frédéric Chyzak, Marni Mishna, and Bruno Salvy, Effective scalar products of D-finite symmetric functions, J. Combin. Theory Ser. A 112 (2005), no. 1, 1-43. MR MR2167474 (2006d:05181) |
[CS98] | Frédéric Chyzak and Bruno Salvy, Non-commutative elimination in Ore algebras proves multivariate identities, J. Symbolic Comput. 26 (1998), no. 2, 187-227. MR MR1635242 (99g:68103) |
[CEP96] | Henry Cohn, Noam Elkies, and James Propp, Local statistics for random domino tilings of the Aztec diamond, Duke Math. J. 85 (1996), no. 1, 117-166. MR MR1412441 (97k:52026) |
[CP] | Harry Cohn and Robin Pemantle, A determination of the boundary of the fixation region for some domino tiling ensembles, in preparation. |
[Com74] | Louis Comtet, Advanced combinatorics, enlarged ed., D. Reidel Publishing Co., Dordrecht, 1974, The art of finite and infinite expansions. MR MR0460128 (57 \#124) |
[CMS98] | Cristiano Corsani, Donatella Merlini, and Renzo Sprugnoli, Left-inversion of combinatorial sums, Proceedings of the 7th Conference on Formal Power Series and Algebraic Combinatorics (Noisy-le-Grand, 1995), vol. 180, 1998, pp. 107-122. MR MR1603705 (99c:05017) |
[CLP04] | Sylvie Corteel, Guy Louchard, and Robin Pemantle, Common intervals of permutations, Mathematics and computer science. III, Trends Math., Birkhäuser, Basel, 2004, pp. 3-14. MR MR2090490 (2005j:60017) |
[CLO05] | David A. Cox, John Little, and Donal O'Shea, Using algebraic geometry, second ed., Graduate Texts in Mathematics, vol. 185, Springer, New York, 2005. MR MR2122859 (2005i:13037) |
[DLS03] | Jesús A. De Loera and Bernd Sturmfels, Algebraic unimodular counting, Math. Program. 96 (2003), no. 2, Ser. B, 183-203, Algebraic and geometric methods in discrete optimization. MR MR1993046 (2004e:90066) |
[DS01] | Emeric Deutsch and Louis Shapiro, A survey of the Fine numbers, Discrete Math. 241 (2001), no. 1-3, 241-265, Selected papers in honor of Helge Tverberg. MR MR1861421 (2002k:05010) |
[DL93] | Ronald A. DeVore and George G. Lorentz, Constructive approximation, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 303, Springer-Verlag, Berlin, 1993. MR MR1261635 (95f:41001) |
[Drm94] | Michael Drmota, A bivariate asymptotic expansion of coefficients of powers of generating functions, European J. Combin. 15 (1994), no. 2, 139-152. MR MR1261060 (94k:05014) |
[Dur96] | Richard Durrett, Probability: theory and examples, second ed., Duxbury Press, Belmont, CA, 1996. MR MR1609153 (98m:60001) |
[Dur04] | , Probability: theory and examples, third ed., Duxbury Press, Belmont, CA, 2004. |
[FIM99] | Guy Fayolle, Roudolf Iasnogorodski, and Vadim Malyshev, Random walks in the quarter-plane, Applications of Mathematics (New York), vol. 40, Springer-Verlag, Berlin, 1999, Algebraic methods, boundary value problems and applications. MR MR1691900 (2000g:60002) |
[Fis61] | Michael E. Fisher, Statistical mechanics of dimers on a plane lattice, Phys. Rev. (2) 124 (1961), 1664-1672. MR MR0136399 (24 \#B2437) |
[FGS06] | Philippe Flajolet, Stefan Gerhold, and Bruno Salvy, On the non-holonomic character of logarithms, powers, and the nth prime function, Electron. J. Combin. 11 (2004/06), no. 2, Article 2, 16 pp. (electronic). MR MR2195433 (2006h:05013) |
[FO90] | Philippe Flajolet and Andrew Odlyzko, Singularity analysis of generating functions, SIAM J. Discrete Math. 3 (1990), no. 2, 216-240. MR MR1039294 (90m:05012) |
[FS] | Phillipe Flajolet and Robert Sedgewick, Analytic combinatorics, in preparation, preprint available at http://algo.inria.fr/flajolet/Publications/book061023.pdf. |
[FS93] | Philippe Flajolet and Michèle Soria, General combinatorial schemas: Gaussian limit distributions and exponential tails, Discrete Math. 114 (1993), no. 1-3, 159-180, Combinatorics and algorithms (Jerusalem, 1988). MR MR1217750 (94e:05021) |
[FH84] | L. Flatto and S. Hahn, Two parallel queues created by arrivals with two demands. I, SIAM J. Appl. Math. 44 (1984), no. 5, 1041-1053. MR MR759714 (86e:60079a) |
[FM77] | L. Flatto and H. P. McKean, Two queues in parallel, Comm. Pure Appl. Math. 30 (1977), no. 2, 255-263. MR MR0464426 (57 \#4356) |
[FHS04] | Abraham Flaxman, Aram W. Harrow, and Gregory B. Sorkin, Strings with maximally many distinct subsequences and substrings, Electron. J. Combin. 11 (2004), no. 1, Research Paper 8, 10 pp. (electronic). MR MR2034422 (2004k:05016) |
[Fur67] | Harry Furstenberg, Algebraic functions over finite fields, J. Algebra 7 (1967), 271-277. MR MR0215820 (35 \#6655) |
[GR92] | Zhicheng Gao and L. Bruce Richmond, Central and local limit theorems applied to asymptotic enumeration. IV. Multivariate generating functions, J. Comput. Appl. Math. 41 (1992), no. 1-2, 177-186, Asymptotic methods in analysis and combinatorics. MR MR1181718 (94b:05017) |
[GW00] | , The distribution of the maximum vertex degree in random planar maps, J. Combin. Theory Ser. A 89 (2000), no. 2, 201-230. MR MR1741015 (2000m:05211) |
[GW99] | Zhicheng Gao and Nicholas C. Wormald, The size of the largest components in random planar maps, SIAM J. Discrete Math. 12 (1999), no. 2, 217-228 (electronic). MR MR1686830 (2000a:05111) |
[Gar95] | Danièle Gardy, Some results on the asymptotic behaviour of coefficients of large powers of functions, Discrete Math. 139 (1995), no. 1-3, 189-217, Formal power series and algebraic combinatorics (Montreal, PQ, 1992). MR MR1336840 (96f:41038) |
[GKZ94] | I. M. Gel'fand, M. M. Kapranov, and A. V. Zelevinsky, Discriminants, resultants, and multidimensional determinants, Mathematics: Theory & Applications, Birkhäuser Boston Inc., Boston, MA, 1994. MR MR1264417 (95e:14045) |
[Ges92] | Ira M. Gessel, Super ballot numbers, J. Symbolic Comput. 14 (1992), no. 2-3, 179-194. MR MR1187230 (93k:05009) |
[GRZ83] | J. Gillis, B. Reznick, and D. Zeilberger, On elementary methods in positivity theory, SIAM J. Math. Anal. 14 (1983), no. 2, 396-398. MR MR688584 (84i:42017) |
[GS00] | Massimiliano Goldwurm and Massimo Santini, Clique polynomials have a unique root of smallest modulus, Inform. Process. Lett. 75 (2000), no. 3, 127-132. MR MR1776664 (2001d:05114) |
[GM88] | Mark Goresky and Robert MacPherson, Stratified Morse theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 14, Springer-Verlag, Berlin, 1988. MR MR932724 (90d:57039) |
[GJ04] | Ian P. Goulden and David M. Jackson, Combinatorial enumeration, Dover Publications Inc., Mineola, NY, 2004, With a foreword by Gian-Carlo Rota, Reprint of the 1983 original. MR MR2079788 (2005b:05001) |
[GH94] | Phillip Griffiths and Joseph Harris, Principles of algebraic geometry, Wiley Classics Library, John Wiley & Sons Inc., New York, 1994, Reprint of the 1978 original. MR MR1288523 (95d:14001) |
[GHOW90] | J. R. Griggs, P. Hanlon, A. M. Odlyzko, and M. S. Waterman, On the number of alignments of k sequences, Graphs Combin. 6 (1990), no. 2, 133-146. MR MR1073683 (91m:92022) |
[GHW86] | Jerrold R. Griggs, Philip J. Hanlon, and Michael S. Waterman, Sequence alignments with matched sections, SIAM J. Algebraic Discrete Methods 7 (1986), no. 4, 604-608. MR MR857596 (87k:05012) |
[GO81b] | Leo J. Guibas and Andrew M. Odlyzko, Periods in strings, J. Combin. Theory Ser. A 30 (1981), no. 1, 19-42. MR MR607037 (83h:68102) |
[GO81a] | L. J. Guibas and A. M. Odlyzko, String overlaps, pattern matching, and nontransitive games, J. Combin. Theory Ser. A 30 (1981), no. 2, 183-208. MR MR611250 (82g:05007) |
[HR17] | G.H. Hardy and S. Ramanujan, Asymptotic formule for the distribution of integers of various types, Proceedings of the London Mathematical Society 16 (1917), 112-132. |
[HK71] | M. L. J. Hautus and D. A. Klarner, The diagonal of a double power series, Duke Math. J. 38 (1971), 229-235. MR MR0276641 (43 \#2383) |
[Hay56] | W. K. Hayman, A generalisation of Stirling's formula, J. Reine Angew. Math. 196 (1956), 67-95. MR MR0080749 (18,293f) |
[Hen88] | , Applied and computational complex analysis. Vol. 1, Wiley Classics Library, John Wiley & Sons Inc., New York, 1988, Power series-integration-conformal mapping-location of zeros, Reprint of the 1974 original, A Wiley-Interscience Publication. MR MR1008928 (90d:30002) |
[Hen91] | , Applied and computational complex analysis. Vol. 2, Wiley Classics Library, John Wiley & Sons Inc., New York, 1991, Special functions-integral transforms-asymptotics-continued fractions, Reprint of the 1977 original, A Wiley-Interscience Publication. MR MR1164865 (93b:30001) |
[Hen86] | Peter Henrici, Applied and computational complex analysis. Vol. 3, Pure and Applied Mathematics (New York), John Wiley & Sons Inc., New York, 1986, Discrete Fourier analysis-Cauchy integrals-construction of conformal maps-univalent functions, A Wiley-Interscience Publication. MR MR822470 (87h:30002) |
[Hör90] | Lars Hörmander, An introduction to complex analysis in several variables, third ed., North-Holland Mathematical Library, vol. 7, North-Holland Publishing Co., Amsterdam, 1990. MR MR1045639 (91a:32001) |
[Hör03] | , The analysis of linear partial differential operators. I, Classics in Mathematics, Springer-Verlag, Berlin, 2003, Distribution theory and Fourier analysis, Reprint of the second (1990) edition [Springer, Berlin; MR1065993 (91m:35001a)]. MR MR1996773 |
[Hwa95] | Hsien-Kuei Hwang, Asymptotic expansions for the Stirling numbers of the first kind, J. Combin. Theory Ser. A 71 (1995), no. 2, 343-351. MR MR1342456 (96k:11019) |
[Hwa96] | , Large deviations for combinatorial distributions. I. Central limit theorems, Ann. Appl. Probab. 6 (1996), no. 1, 297-319. MR MR1389841 (97g:60041) |
[Hwa98a] | , Large deviations of combinatorial distributions. II. Local limit theorems, Ann. Appl. Probab. 8 (1998), no. 1, 163-181. MR MR1620350 (99i:60056) |
[Hwa98b] | , On convergence rates in the central limit theorems for combinatorial structures, European J. Combin. 19 (1998), no. 3, 329-343. MR MR1621021 (99c:60014) |
[Kit03] | Sergey Kitaev, Generalized patterns in words and permutations, Ph.D. thesis, Chalmers University of Technology and Göteborg University, 2003. |
[Kog02] | Yaakov Kogan, Asymptotic expansions for large closed and loss queueing networks, Math. Probl. Eng. 8 (2002), no. 4-5, 323-348. MR MR1960960 (2003k:90013) |
[KY96] | Yaakov Kogan and Andrei Yakovlev, Asymptotic analysis for closed multichain queueing networks with bottlenecks, Queueing Systems Theory Appl. 23 (1996), no. 1-4, 235-258. MR MR1433772 (97i:60122) |
[KMM02] | Daniel Krob, Jean Mairesse, and Ioannis Michos, On the average parallelism in trace monoids, STACS 2002, Lecture Notes in Comput. Sci., vol. 2285, Springer, Berlin, 2002, pp. 477-488. MR MR2050861 |
[KMM03] | , Computing the average parallelism in trace monoids, Discrete Math. 273 (2003), no. 1-3, 131-162, EuroComb'01 (Barcelona). MR MR2025946 (2005a:05009) |
[LL99] | Michael Larsen and Russell Lyons, Coalescing particles on an interval, J. Theoret. Probab. 12 (1999), no. 1, 201-205. MR MR1674992 (2000j:60012) |
[Ler59] | Jean Leray, Le calcul différentiel et intégral sur une variété analytique complexe. (Problème de Cauchy. III), Bull. Soc. Math. France 87 (1959), 81-180. MR MR0125984 (23 \#A3281) |
[Li80] | Shuo-Yen Robert Li, A martingale approach to the study of occurrence of sequence patterns in repeated experiments, Ann. Probab. 8 (1980), no. 6, 1171-1176. MR MR602390 (82c:60018) |
[Lic91] | Ben Lichtin, The asymptotics of a lattice point problem associated to a finite number of polynomials. I, Duke Math. J. 63 (1991), no. 1, 139-192. MR MR1106941 (93d:11107) |
[Lic95] | , The asymptotics of a lattice point problem associated to a finite number of polynomials. II, Duke Math. J. 77 (1995), no. 3, 699-751. MR MR1324639 (96b:11134) |
[Lip88] | L. Lipshitz, The diagonal of a D-finite power series is D-finite, J. Algebra 113 (1988), no. 2, 373-378. MR MR929767 (89c:13027) |
[Lla03] | , Asymptotic enumeration via singularity analysis, Ph.D. thesis, The Ohio State University, 2003. |
[Lla] | Manuel Lladser, Uniform formulae for coefficients of meromorphic functions in two variables, in preparation. |
[MM90] | A. Meir and J. W. Moon, The asymptotic behaviour of coefficients of powers of certain generating functions, European J. Combin. 11 (1990), no. 6, 581-587. MR MR1078714 (91m:05014) |
[MRSV97] | Donatella Merlini, Douglas G. Rogers, Renzo Sprugnoli, and M. Cecilia Verri, On some alternative characterizations of Riordan arrays, Canad. J. Math. 49 (1997), no. 2, 301-320. MR MR1447493 (98m:05008) |
[MSV94] | Donatella Merlini, Renzo Sprugnoli, and M. Cecilia Verri, Algebraic and combinatorial properties of simple, coloured walks, Trees in algebra and programming-CAAP '94 (Edinburgh, 1994), Lecture Notes in Comput. Sci., vol. 787, Springer, Berlin, 1994, pp. 218-233. MR MR1286762 (95d:05008) |
[MSV96] | , A uniform model for the storage utilization of B-tree-like structures, Inform. Process. Lett. 57 (1996), no. 1, 53-58. MR MR1374700 (96j:68043) |
[MV00] | Donatella Merlini and M. Cecilia Verri, Generating trees and proper Riordan arrays, Discrete Math. 218 (2000), no. 1-3, 167-183. MR MR1754333 (2001f:05009) |
[Mum95] | David Mumford, Algebraic geometry. I, Classics in Mathematics, Springer-Verlag, Berlin, 1995, Complex projective varieties, Reprint of the 1976 edition. MR MR1344216 (96d:14001) |
[MZS04] | Emanuele Munarini and Norma Zagaglia Salvi, Binary strings without zigzags, Sém. Lothar. Combin. 49 (2002/04), Art. B49h, 15 pp. (electronic). MR MR2050271 (2005a:05011) |
[Nkw03] | Asamoah Nkwanta, A Riordan matrix approach to unifying a selected class of combinatorial arrays, Proceedings of the Thirty-Fourth Southeastern International Conference on Combinatorics, Graph Theory and Computing, vol. 160, 2003, pp. 33-45. MR MR2049101 (2005b:05015) |
[Odl95] | A. M. Odlyzko, Asymptotic enumeration methods, Handbook of combinatorics, Vol.1,2, Elsevier, Amsterdam, 1995, pp. 1063-1229. MR MR1373678 (97b:05012) |
[PW00] | Paul Peart and Wen-jin Woan, A divisibility property for a subgroup of Riordan matrices, Discrete Appl. Math. 98 (2000), no. 3, 255-263. MR MR1733675 (2000j:05006) |
[Pem00] | , Generating functions with high-order poles are nearly polynomial, Mathematics and computer science (Versailles, 2000), Trends Math., Birkhäuser, Basel, 2000, pp. 305-321. MR MR1798308 (2002k:05011) |
[Pem] | Robin Pemantle, Asymptotics of multivariate generating functions, lecture notes, available at http://www.math.upenn.edu/~pemantle/Asymptotics.html. |
[PW02] | Robin Pemantle and Mark C. Wilson, Asymptotics of multivariate sequences. I. Smooth points of the singular variety, J. Combin. Theory Ser. A 97 (2002), no. 1, 129-161. MR MR1879131 (2003a:05015) |
[PW04] | , Asymptotics of multivariate sequences. II. Multiple points of the singular variety, Combin. Probab. Comput. 13 (2004), no. 4-5, 735-761. MR MR2095981 (2005i:05008) |
[PWb] | , Twenty combinatorial examples of asymptotics derived from multivariate generating functions, submitted, preprint available at http://arxiv.org/pdf/math.CO/0512548. |
[PWa] | Robin Pemantle and Mark C. Wilson, Asymptotic expansions of Fourier-Laplace integrals, in preparation. |
[PS05] | T. Kyle Petersen and David Speyer, An arctic circle theorem for Groves, J. Combin. Theory Ser. A 111 (2005), no. 1, 137-164. MR MR2144860 |
[Pip01] | Nicholas Pippenger, Enumeration of equicolorable trees, SIAM J. Discrete Math. 14 (2001), no. 1, 93-115 (electronic). MR MR1814540 (2001j:05073) |
[Pól69] | G. Pólya, On the number of certain lattice polygons, J. Combinatorial Theory 6 (1969), 102-105. MR MR0236031 (38 \#4329) |
[LPŠ+] | Manuel E. Lladser, Primoz Potocnik, Jana Šiagiová, Jozef Širán, and Mark C. Wilson, The diameter of random Cayley digraphs of given degree, Submitted to Random Structures and Algorithms, 2006. |
[RW] | Alexanader Raichev and Mark C. Wilson, A new diagonal method for aymptotics of multivariate sequences, in preparation. |
[RT] | M. Régnier and F. Tahi, Generating functions in computational biology, preprint available at http://algo.inria.fr/regnier/publis/ReTa04.ps. |
[Rio68] | John Riordan, Combinatorial identities, John Wiley & Sons Inc., New York, 1968. MR MR0231725 (38 \#53) |
[Rog78] | D. G. Rogers, Pascal triangles, Catalan numbers and renewal arrays, Discrete Math. 22 (1978), no. 3, 301-310. MR MR522725 (80g:05008) |
[SGWW91] | Louis W. Shapiro, Seyoum Getu, Wen Jin Woan, and Leon C. Woodson, The Riordan group, Discrete Appl. Math. 34 (1991), no. 1-3, 229-239, Combinatorics and theoretical computer science (Washington, DC, 1989). MR MR1137996 (92j:05117) |
[Spr94] | Renzo Sprugnoli, Riordan arrays and combinatorial sums, Discrete Math. 132 (1994), no. 1-3, 267-290. MR MR1297386 (96b:05018) |
[Spr95] | , Riordan arrays and the Abel-Gould identity, Discrete Math. 142 (1995), no. 1-3, 213-233. MR MR1341448 (96f:05014) |
[Sta97] | Richard P. Stanley, Enumerative combinatorics. Vol. 1, Cambridge Studies in Advanced Mathematics, vol. 49, Cambridge University Press, Cambridge, 1997, With a foreword by Gian-Carlo Rota, Corrected reprint of the 1986 original. MR MR1442260 (98a:05001) |
[Sta99] | , Enumerative combinatorics. Vol. 2, Cambridge Studies in Advanced Mathematics, vol. 62, Cambridge University Press, Cambridge, 1999, With a foreword by Gian-Carlo Rota and appendix 1 by Sergey Fomin. MR MR1676282 (2000k:05026) |
[Ste93] | Elias M. Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton Mathematical Series, vol. 43, Princeton University Press, Princeton, NJ, 1993, With the assistance of Timothy S. Murphy, Monographs in Harmonic Analysis, III. MR MR1232192 (95c:42002) |
[Stu05] | Bernd Sturmfels, What is ...a Gröbner basis?, Notices Amer. Math. Soc. 52 (2005), no. 10, 1199-1200. MR MR2186903 |
[Tsi91] | A. K. Tsikh, Conditions for absolute convergence of series of Taylor coefficients of meromorphic functions of two variables, Mat. Sb. 182 (1991), no. 11, 1588-1612. MR MR1137864 (92h:32003) |
[vdHP] | Joris van der Hoeven and Robin Pemantle, Automatic computation of asymptotics of coefficients of bivariate rational generating functions, in preparation. |
[Was65] | Wolfgang Wasow, Asymptotic expansions for ordinary differential equations, Pure and Applied Mathematics, Vol. XIV, Interscience Publishers John Wiley & Sons, Inc., New York-London-Sydney, 1965. MR MR0203188 (34 \#3041) |
[Wat95] | Michael S. Waterman, Applications of combinatorics to molecular biology, Handbook of combinatorics, Vol.1,2, Elsevier, Amsterdam, 1995, pp. 1983-2001. MR MR1373695 (97e:92003) |
[Wil06] |
Herbert S. Wilf, generatingfunctionology, third ed., A K Peters Ltd.,
Wellesley, MA, 2006, available at
http://www.math.upenn.edu/%7Ewilf/DownldGF.html. MR MR2172781
An excellent introduction to generating functions. |
[Wil94] | , generatingfunctionology, second ed., Academic Press Inc., Boston, MA, 1994. MR MR1277813 (95a:05002) |
[Wil90] | Herbert S. Wilf, generatingfunctionology, Academic Press Inc., Boston, MA, 1990. MR MR1034250 (91g:05008) |
[Wil05] | Mark C. Wilson, Asymptotics for generalized Riordan arrays, 2005 International Conference on Analysis of Algorithms, Discrete Math. Theor. Comput. Sci. Proc., AD, Assoc. Discrete Math. Theor. Comput. Sci., Nancy, 2005, pp. 323-333 (electronic). MR MR2193129 |
[Woj06] | John Wojdylo, Computing the coefficients in Laplace's method, SIAM Rev. 48 (2006), no. 1, 76-96 (electronic). MR MR2219312 |
[Won01] | R. Wong, Asymptotic approximations of integrals, Classics in Applied Mathematics, vol. 34, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2001, Corrected reprint of the 1989 original. MR MR1851050 (2002f:41023) |
[Wor] | Nicholas C. Wormald, Tournaments with many Hamilton cycles, in preparation. |
[Zei90] | Doron Zeilberger, A holonomic systems approach to special functions identities, J. Comput. Appl. Math. 32 (1990), no. 3, 321-368. MR MR1090884 (92b:33014) |
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