An identity for second Eulerian numbers via lattice-point counting
Combinatorics
2026-05-26 v1
Abstract
The second Eulerian numbers are defined via the descent enumerator of Stirling permutations, a class of permutations introduced by Gessel and Stanley. We give a simple and conceptual proof of two identities relating the Bernoulli numbers and the second Eulerian numbers. We rely on a recent Ehrhart-theoretic idea of Ferroni.
Cite
@article{arxiv.2605.24586,
title = {An identity for second Eulerian numbers via lattice-point counting},
author = {Jack Boncompagni},
journal= {arXiv preprint arXiv:2605.24586},
year = {2026}
}
Comments
14 pages, 5 figures