Two-Sided Eulerian Numbers

Authors

Haven Wagner, The College of WoosterFollow

Abstract

The Eulerian numbers count the number of permutations in the symmetric groups with a certain number of descents. The generating function for the Eulerian numbers can be sorted into terms that correspond to equivalence classes partitioned by the particularly elegant “valley-hopping” proof. The two-sided Eulerian numbers are an analog of the Eulerian numbers that also count the number descents of each permutation’s inverse. Gessel’s conjecture sorts the generating function for the two-sided Eulerian numbers, and it has been proven using recurrence relations, but a proof that matches the valley-hopping proof in elegance is yet to be found.

Advisor

Moynihan, Matthew

Department

Mathematics

Recommended Citation

Wagner, Haven, "Two-Sided Eulerian Numbers" (2017). Senior Independent Study Theses. Paper 7488.
https://openworks.wooster.edu/independentstudy/7488

Disciplines

Discrete Mathematics and Combinatorics

Publication Date

2017

Degree Granted

Bachelor of Arts

Document Type

Senior Independent Study Thesis