Identities of the multi-variate independence polynomials from heaps theory
Combinatorics
2025-05-21 v1
Abstract
We study and derive identities for the multi-variate independence polynomials from the perspective of heaps theory. Using the inversion formula and the combinatorics of partially commutative algebras we show how the multi-variate version of Godsil type identity as well as the fundamental identity can be obtained from weight preserving bijections. Finally, we obtain a new multi-variate identity involving connected bipartite subgraphs similar to the Christoffel-Darboux type identities obtained by Bencs.
Keywords
Cite
@article{arxiv.2209.08029,
title = {Identities of the multi-variate independence polynomials from heaps theory},
author = {Deniz Kus and Kartik Singh and R. Venkatesh},
journal= {arXiv preprint arXiv:2209.08029},
year = {2025}
}