Independence Polynomials of 2-step Nilpotent Lie Algebras
Rings and Algebras
2026-05-13 v2 Combinatorics
Quantum Physics
Abstract
Motivated by the Dani-Mainkar construction, we extend the notion of independence polynomial of graphs to arbitrary 2-step nilpotent Lie algebras. After establishing efficiently computable upper and lower bounds for the independence number, we discuss a metric-dependent generalization motivated by a quantum mechanical interpretation of our construction. As an application, we derive elementary bounds for the dimension of abelian subalgebras of 2-step nilpotent Lie algebras.
Keywords
Cite
@article{arxiv.2504.19836,
title = {Independence Polynomials of 2-step Nilpotent Lie Algebras},
author = {Marco Aldi and Thor Gabrielsen and Daniele Grandini and Joy Harris and Kyle Kelley},
journal= {arXiv preprint arXiv:2504.19836},
year = {2026}
}