Speaker:  Kyle Petersen, DePaul University
Title: The zig-zag Eulerian polynomial
Time: 2:30 PM, Monday, October 16, 2023
Place:  Malott 206

Abstract: For any finite partially ordered set $P$, the $P$-Eulerian polynomial is the generating function for descents over the set of linear extensions of $P$. Here we study the $Z_n$-Eulerian polynomials, where $Z_n$ denotes a naturally labeled zig-zag poset on $n$ elements. By a result of Brändén, these polynomials are gamma-nonnegative, and hence the coefficients are symmetric and unimodal. These polynomials have appeared directly or indirectly in about half a dozen distinct contexts (from magic labelings of graphs to the study of hydrocarbons), but have not been studied systematically. We will survey new and old results, and point to some open questions. This work is joint with Yan Zhuang.


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