Séminaire Lotharingien de Combinatoire, 93B.100 (2025), 12 pp.
Jerónimo Valencia Porras
A Combinatorial Proof of an Identity Involving Eulerian Numbers
Abstract.
We give a combinatorial proof of an identity that involves Eulerian numbers and was obtained algebraically by Brenti and Welker (2009). To do so, we study alcoved triangulations of dilated hypersimplices. As a byproduct, we describe the dual graph of these triangulations for the dilated standard simplex and the hypersimplex in terms of combinatorial objects, and conjecture their structure for dilated hypersimplices.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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