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CAGE: Philadelphia Area Combinatorics and Alg. Geometry Seminar

Thursday, January 31, 2019 - 3:00pm

Sean Griffin

Univ. of Washington


University of Pennsylvania


In 1995, Gessel introduced a multivariate formal power series tracking the distribution of ascents and descents in labeled binary trees. In addition to showing that it was a symmetric function, he conjectured it was Schur-positive. In this talk, we show how to expand this symmetric function positively in terms of ribbon Schur functions. In fact, a refinement of this conjecture holds. We get a family of Schur-positive functions indexed by certain intervals in the Tamari lattice. I will also present our progress in constructing the corresponding symmetric group representations and how certain specializations of the symmetric function relate to actions on hyperplane arrangements. Finally, I will show how our work specializes to a proof of gamma-positivity of the distribution of right descents over local binary search trees.
This is joint work with Ira Gessel and Vasu Tewari.