# Ira M Gessel

Degrees

Massachusetts Institute of Technology, Ph.D.Harvard University, B.A.

Expertise

Combinatorics.Profile

My research is in enumerative combinatorics, which involves counting objects such as permutations, partitions, graphs and lattice paths. WebpageCourses Taught

MATH | 23b | Introduction to Proofs |

MATH | 100a | Introduction to Algebra, Part I |

MATH | 101a | Algebra I |

MATH | 108b | Number Theory |

MATH | 141b | Complex Analysis |

MATH | 180a | Combinatorics |

Awards and Honors

Fellow of the American Mathematical Society (2013)

Scholarship

Gessel, Ira M. "A simple proof of Andrews's 5F4 evaluation." __Ramanujan Journal__ 36. (2015): 165–170.

Gessel, Ira M; Levine, Adam Simon; Ruberman, Daniel; Strle, Saso. "Non-orientable surfaces in homology cobordisms." __Geom. Topol.__ 19. (2015): 439–494.

Gessel, Ira M; Zhuang, Yan. "Counting permutations by alternating descents." __Electronic J. Combin.__ 2014. 4 (2015): #P4.23.

Gessel, Ira M. "A short proof of the Deutsch-Sagan congruence for connected noncrossing graphs." (2014): <arXiv:1403.7656>.

Gessel, Ira M; Gainer-Dewar, Andrew. "Counting unlabeled k-trees." __J. Combin. Theory Ser. A__ 126. (2014): 177–193.

Gessel, Ira M; Gainer-Dewar, Andrew. "Enumeration of bipartite graphs and bipartite blocks." __Electronic J. Combin.__ 21. 2 (2014): #P2.40.

Belbachir; Hacene; Gessel, Ira M; Rahmani, Mourad. "On Gessel-Kaneko’s identity for Bernoulli numbers." __Applicable Analysis and Discrete Mathematics__ 7. (2013): 1-10.

Gessel, Ira M. (with Ji Li). "Compositions and Fibonacci identities." __Journal of Integer Sequences__ 16. 4 (2013): Article 13.4.5.

Gessel, Ira M. (with Zhicong Lin and Jiang Zeng). "Jacobi-Stirling polynomials and P-partitions." __European J. Combinatorics__ 33. (2012): 1987–2000.

Gessel, Ira M. (with A. Restivo and C. Reutenauer). "A bijection between words and multisets of necklaces." __European J. Combinatorics__ 33. (2012): 1537–1546.

Gessel, Ira M. (with Ji Li). "Enumeration of point-determining graphs." __J. Combinatorial Theory Ser. A__ 118. (2011): 591–612.

Gessel, Ira M. (with Paul Monsky). "The limit as p → ∞ of the Hilbert-Kunz multiplicity of sum(x_i^(d_i))." __arXiv__ (2011): <arXiv:1007.2004>.

Gessel, Ira M. (with Jang Soo Kim). "A note on 2-distant noncrossing partitions and weighted Motzkin paths." __Discrete Math.__ 310. (2010): 3421–3425.

Gessel, Ira M. (with Matthias Beck, Sunyoung Lee, and Carla D. Savage). "Symmetrically constrained compositions." __Ramanujan Journal__ 23. (2010): 355–369.

Gessel, Ira M. (with Nicholas Loehr). "Note on enumeration of partitions contained in a given shape." __Linear Algebra Appl.__ 432. (2010): 583–585.

Gessel, Ira M., with Pallavi Jayawant. "Multilinear generating functions for Charlier polynomials." __J. Statist. Inf. Plann.__ (2010): 2230–2236.

Gessel, Ira M. (with Peter J. Larcombe). "The sum $\sum_{k=0}^{2n} 4^k \binom{1/2}{k}\binom{-1/2}{k}\binom{-2k}{2n-k}$; a third proof of its closed form." __Util. Math.__ 80. 59–63 (2009).

Gessel, Ira M., with Lun Lv, Guoce Xin, and Yue Zhou. "A unified elementary approach to the Dyson, Morris, Aomoto, and Forrester constant term identities." __J. Combin. Theory Ser. A__ 115. (2008): 1417-1435.

Gessel, Ira M., with William Y. C. Chen, Arthur L.B. Yang, and Catherine H. Yan. "A major statistic for matchings and partitions." __J. Combin. Theory Ser. A__ 115. (2008): 1069-1076.

Gessel, Ira M., with Brian Drake and Guoce Xin. "Three proofs of the Goulden-Litsyn-Shevelev conjecture on a sequence arising in algebraic geometry." __J. Integer Sequences__ 10. 3 (2007): Article 07.3.7.

Gessel, Ira M., with Chak-On Chow. "On the descent numbers and major indices for the hyperoctahedral group." __Adv. in Applied Math.__ 38. (2007): 275-301.

Gessel, Ira M., with Sylvie D. Corteel, Carla Savage, and Herbert S. Wilf. "The joint distribution of descent and major index over restricted sets of permutations." __Annals of Combinatorics__ 11. (2007): 375-386.

Gessel, Ira M. "Symmetric inclusion-exclusion." __Séminaire Lotharingien de Combinatoire__ 54. (2006): Art. B54b, 10 pp

Gessel, Ira M., with Guoce Xin. "A short proof of the Zeilberger-Bressoud q-Dyson theorem." __Trans. Amer. Math. Soc.__ 134. (2006): 2179-2187.

Gessel, Ira M., with Guoce Xin. "The generating function of ternary trees and continued fractions." __Electronic J. Combinatorics__ 13. 1 (2006): R5

Gessel, Ira M., with Senghyun Seo. "A refinement of Cayley's formula for trees." __Electronic J. Combinatorics__ 11. 2 (2006): R2

Gessel,Ira M with Guoce Xin. "A combinatorial interpretation of the numbers 6 (2n)!/n!(n+2)!." __J. Integer Sequences__ 8. 2 (2005): Article 05.2.3, 13 pp..

Gessel,Ira M with Louis Kalikow. "Hypergraphs, hypertrees and expansions of some formal power series." __J. Combin. Theory Ser. A__ (2005).

Gessel,Ira M with Ron M. Adin and Yuval Roichman. "Signed Mahonians." __J. Combin. Theory Ser. A 109__ (2005): 25-43.

Gessel,Ira M. "On Miki's identity for Bernoulli numbers." __J. Number Theory 110__ (2005): 75-82.

Gessel,Ira M. "Applications of the classical umbral calculus." __Algebra Universalis__ 49. (2003): 397-434.