Ira Gessel's Electronically Available Papers

 

Counting unlabeled k-trees (with Andrew Gainer-Dewar), preprint, 2013.
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Enumeration of bipartite graphs and bipartite blocks (with Andrew Gainer-Dewar), preprint, 2013.
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A simple proof of Andrews's 5F4 evaluation, preprint, 2013.
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Compositions and Fibonacci identities (with Ji Li), J. Integer Sequences, Article 13.4.5, 2013.
Link to JIS,

Jacobi-Stirling polynomials and P-partitions (with Zhicong Lin and Jiang Zeng), European J. Combin. 33 (2012), 1987–2000.
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A bijection between words and multisets of necklaces (with A. Restivo and C. Reutenauer), European J. Combin. 33 (2012), 1537–1546.
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Enumeration of point-determining graphs (with Ji Li), J. Combinatorial Theory Ser. A 118 (2011), 591–612.
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The limit as p -> infinity of the Hilbert-Kunz multiplicity of sum(x_i^(d_i))i (with Paul Monsky), arXiv:1007.2004, 2010.

A note on 2-distant noncrossing partitions and weighted Motzkin paths (with Jang Soo Kim), Discrete Math., 310 (2010), 3421–3425.
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Symmetrically constrained compositions (with Matthias Beck, Sunyoung Lee, and Carla D. Savage), Ramanujan Journal 23 (2010), 355–369.
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Note on enumeration of partitions contained in a given shape (with Nicholas Loehr), Linear Algebra Appl. 432 (2010), 583–585.
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Multilinear generating functions for Charlier polynomials (with Pallavi Jayawant), J. Statist. Inf. Plann. 140 (2010), 2230–2236.
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The sum complicated formula : a third proof of its closed form (with Peter J. Larcombe), Util. Math. 80 (2009), 59–63.
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A major statistic for matchings and partitions (with William Y. C. Chen, Arthur L.B. Yang, and Catherine H. Yan), J. Combin. Theory Ser. A, 115 (2008), 1069–1076.
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A unified elementary approach to the Dyson, Morris, Aomoto, and Forrester constant term identities (with Lun Lv, Guoce Xin, and Yue Zhou), J. Combin. Theory Ser. A, 115 (2008), 1417–1435.
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The joint distribution of descent and major index over restricted sets of permutations (with Sylvie D. Corteel, Carla Savage, and Herbert S. Wilf), Annals of Combinatorics 11 (2007), 375–386.
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Three proofs and a generalization of the Goulden-Litsyn-Shevelev conjecture on a sequence arising in algebraic geometry (with Brian Drake and Guoce Xin), J. Integer Seq. 10 (2007), Article 07.3.7.
Link to JIS

On the descent numbers and major indices for the hyperoctahedral group (with Chak-On Chow), Adv. in Appl. Math. 38 (2007), 275–301.
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A refinement of Cayley's formula for trees (with Seunghyun Seo), Electronic J. Combinatorics 11, no. 2 (2004–2006), R27.
Link to E-JC

A short proof of the Zeilberger-Bressoud q-Dyson theorem (with Guoce Xin), Proc. Amer. Math. Soc. 134 (2006), 2179–2187.
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The generating function of ternary trees and continued fractions (with Guoce Xin), Electronic J. Combinatorics 13, no. 1 (2006), R53.
Link to E-JC

Symmetric inclusion-exclusion, Séminaire Lotharingien de Combinatorie 54 (2005), B54b.
Link to SLC

A combinatorial interpretation of the numbers 6(2n)! /n! (n+2)! (with Guoce Xin), J. Integer Seq. 8 (2005), no. 2, Article 05.2.3, 13 pp.
Link to JIS

A triple lacunary generating function for Hermite polynomials (with Pallavi Jayawant), Electronic Journal of Combinatorics 12 (2005), Research Paper 30, 14 pp.
Link to E-JC

Hypergraphs and a functional equation of Bouwkamp and de Bruijn (with Louis H. Kalikow) J. Combinatorial Theory, Ser. A 110 (2005), 275–289.
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On Miki's identity for Bernoulli numbers, J. Number Theory, 110 (2005), 75–82.
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Signed Mahonians (with Ron M. Adin and Yuval Roichman), J. Combin. Theory Ser. A 109 (2005), 25–43.
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Slides from a talk on Rational functions with nonnegative power series coefficients, 50th Seminaire Lotharingien de Combinatoire, March 25, 2003.
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Applications of the classical umbral calculus Algebra Universalis 49 (2003), 397–434.
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The polynomial part of a restricted partition function related to the Frobenius problem (with Matthias Beck and Takao Komatsu) Electronic J. Combinatorics 8 (2001), No. 1, N7 (5 pages).
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Link to E-JC

The specification of 2-trees (with Tom Fowler, Gilbert Labelle, and Pierre Leroux), Advances in Applied Math. 28 (2002), 145–168.
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Acyclic orientations and chromatic generating functions, Discrete Math. 232 (2001), 119–130.
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On the order of Stirling numbers and alternating binomial coefficient sums (with Tamas Lengyel), Fibonacci Quarterly, 39 (2001), 444–454.
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The Smith College diploma problem, Amer. Math. Monthly 108 (2001), 55–57.
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On the number of convex polyominoes, Annales des Sciences Mathemathiques du Quebec, 24 (2000), 63–66.
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Tilings of diamonds and hexagons with defects (with Harald Helfgott),Electronic J. Combinatorics 6, No. 1 (1999), R16 (21 pages).
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Wolstenholme revisited Amer. Math. Monthly 105 (1998), 657–658.
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Lattice walks in Zd and permutations with no long ascending subsequences (with Jonathan Weinstein and Herbert S. Wilf), Electronic J. Combinatorics 5, No. 1 (1998), R2 (11 pages).
Link to EJC

Lattice paths and Faber polynomials (with Sangwook Ree), in Advances in Combinatorial Methods and Applications to Probability and Statistics, ed. N. Balakrishnan, Birkhauser Boston, 1997, pp. 3–13.
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Cylindric partitions (with C. Krattenthaler), Trans. Amer. Math. Soc. 349 (1997), 429–479.
Link to TAMS

Generating functions and generalized Dedekind sums, Electronic J. Combinatorics 4, No. 2, Wilf Festschrift (1997), R11 (17 pages).
Link to EJC

Even and odd pairs of lattice paths with multiple intersections (with Walter Shur), J. Combin. Theory Ser. A 75 (1996), 243–253.
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Counting pairs of lattice paths by intersections (with Wayne Goddard, Walter Shur, Herbert S. Wilf, and Lily Yen), J. Combin. Theory Ser. A 74 (1996), 173–187.
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The Tutte polynomial of a graph, depth-first search, and simplicial complex partitions (with Bruce Sagan), Electronic J. Combinatorics 3, No. 2, Foata Festschrift (1996), R9 (36 pages).
Link to EJC

Counting forests by descents and leaves, Electronic J. Combinatorics 3, No. 2, Foata Festschrift (1996), R8 (5 pages).
Link to EJC

Counting acyclic digraphs by sources and sinks, Discrete Math. 160 (1996), 253–258.
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Enumerative applications of a decomposition for graphs and digraphs, Discrete Math. 139 (1995), 257–271.
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Lagrange inversion for species, (with G. Labelle), J. Combin. Theory Ser. A 72 (1995), 95–117.
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Algebraic enumeration (with R. P. Stanley), in Handbook of Combinatorics ed. R. L. Graham, M. Grotschel, and L. Lovasz, Elsevier and MIT Press, 1995, pp. 1021–1062.
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Finding identities with the WZ method., J. Symbolic Comput. 20 (1995), 537–566.
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Counting paths in Young's lattice, J. Statistical Planning and Inference 34 (1993), 125–134.
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Super ballot numbers, J. Symbolic Computation 14 (1992), 179–194.
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A coloring problem, Amer. Math. Monthly 98 (1991), 530–533.
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Symmetric functions and P-recursiveness, J. Combin. Theory Ser. A 53 (1990), 257–285.
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Generalized rook polynomials and orthogonal polynomials, in q-Series and Partitions, ed. D. Stanton, The IMA Volumes in Mathematics and Its Applications, Vol. 18, Springer-Verlag, New York, 1989, pp. 159–176.
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Determinants, paths, and plane partitions (with X. G. Viennot), preprint, 1989
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Enumerative applications of symmetric functions, Séminaire Lotharingien de Combinatoire B17a (1987), 17 pp.
Link to SLC

Counting three-line Latin rectangles, in Combinatoire énumerative, ed. G. Labelle and P. Leroux, Lecture Notes in Mathematics, Vol. 1234, Springer-Verlag, 1986, pp. 106–111.
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A probabilistic method for lattice path enumeration, J. Statist. Plann. Inference 14 (1986), 49–58.
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Combinatorial proofs of congruences, in Enumeration and Design, ed. David M. Jackson and Scott A. Vanstone, Academic Press, Toronto, 1984, pp. 157–197.
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Multipartite P-partitions and inner products of skew Schur functions, Contemp. Math. 34 (1984), 289–301.
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Some congruences for generalized Euler numbers, Canad. J. Math. 35 (1983), 687–709.
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A factorization for formal Laurent series and lattice path enumeration J. Combin. Theory Ser. A 28 (1980), 321–337.
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Permutation statistics and partitions (with A. M. Garsia), Adv. in Math. 31 (1979), 288–305.
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Generating Functions and Enumeration of Sequences, Ph.D. Thesis, Massachusetts Institute of Technology, 1977.
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