English

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.

Keywords

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

R2 v1 2026-07-22T07:30:04.440Z