Local h-polynomials, uniform triangulations and real-rootedness

Seminar
Speaker
Christos Athanasiadis (Univ. of Athens)
Date
12/05/2024 - 19:00 - 18:00Add to Calendar 2024-05-12 18:00:00 2024-05-12 19:00:00 Local h-polynomials, uniform triangulations and real-rootedness Link to the recording The local h-polynomial is a fundamental enumerative invariant of a triangulation Δ of a simplex. This talk aims to review its remarkable combinatorial properties, discuss nice examples and address the following question: Which triangulations of the simplex have a real-rooted h-polynomial? Our main result states that this is the case when Δ is the barycentric subdivision of any triangulation of the simplex. The proof is based on a new combinatorial formula for the local h-polynomial, which is valid when Δ is any uniform triangulation of any triangulation of the simplex, and on the study of a family of polynomials which refine and interpolate between Eulerian and derangement polynomials. A combinatorial interpretation of the local h-polynomial of the second barycentric subdivision of the simplex will be deduced. ZOOM אוניברסיטת בר-אילן - המחלקה למתמטיקה mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
ZOOM
Abstract

Link to the recording

The local h-polynomial is a fundamental enumerative invariant
of a triangulation Δ of a simplex. This talk aims to review its
remarkable combinatorial properties, discuss nice examples and address
the following question: Which triangulations of the simplex have a
real-rooted h-polynomial? Our main result states that this is the case
when Δ is the barycentric subdivision of any triangulation of the
simplex. The proof is based on a new combinatorial formula for the
local h-polynomial, which is valid when Δ is any uniform triangulation
of any triangulation of the simplex, and on the study of a family of
polynomials which refine and interpolate between Eulerian and
derangement polynomials. A combinatorial interpretation of the local
h-polynomial of the second barycentric subdivision of the simplex will
be deduced.

תאריך עדכון אחרון : 17/06/2024