Ira M Gessel

Professor Emeritus of Mathematics

Departments/Programs

Computer Science
Mathematics

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. Webpage

Courses Taught

MATH	23b	Introduction to Proofs
MATH	100a	Introduction to Algebra, Part 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.