English

Wiener Indices of Minuscule Lattices

Combinatorics 2023-04-14 v1

Abstract

The Wiener index of a finite graph G is the sum over all pairs (p, q) of vertices of G of the distance between p and q. When P is a finite poset, we define its Wiener index as the Wiener index of the graph of its Hasse diagram. In this paper, we find exact expressions for the Wiener indices of the distributive lattices of order ideals in minuscule posets. For infinite families of such posets, we also provide results on the asymptotic distribution of the distance between two random order ideals.

Keywords

Cite

@article{arxiv.2304.06113,
  title  = {Wiener Indices of Minuscule Lattices},
  author = {Colin Defant and Valentin Féray and Philippe Nadeau and Nathan Williams},
  journal= {arXiv preprint arXiv:2304.06113},
  year   = {2023}
}

Comments

16 pages, 5 figures