Riordan pattern's quest within simplicial complexes
Combinatorics
2025-07-15 v1
Abstract
The aim of this paper is twofold. First, we demonstrate how Riordan matrices can be employed to connect well-known concepts in geometric combinatorics, such as -vectors, -vectors -vectors, in a similar fashion to the McMullen Correspondence, and the Dehn-Sommerville equations, among others. Second, we investigate the combinatorial properties of the topological join operation, both for simplicial complexes and for Alexandroff spaces. Finally, we explore the Riordan matrices arising from the iteration of this topological operation and analyze their properties.
Cite
@article{arxiv.2507.09504,
title = {Riordan pattern's quest within simplicial complexes},
author = {Pedro J. Chocano and Ana Luzón and Manuel A. Morón and Luis Felipe Prieto-Martínez},
journal= {arXiv preprint arXiv:2507.09504},
year = {2025}
}