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arXiv · 2504.19836

Independence Polynomials of 2-step Nilpotent Lie Algebras

Marco Aldi·Thor Gabrielsen·Daniele Grandini·Joy Harris·Kyle Kelley
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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.

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Marco Aldi, Thor Gabrielsen, Daniele Grandini, Joy Harris, Kyle Kelley. 2025-04-28. Independence Polynomials of 2-step Nilpotent Lie Algebras. https://arxiv.org/abs/2504.19836

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