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Joy Harris

Publications and source records attributed to Joy Harris.

2 recordsLinked to original sources
arXiv2026

An Efficiently Computable Lower Bound for the Independence Number of Hypergraphs

Let $k\ge2$ be fixed. We study the integer lower bound $\ell(G)$ obtained by inverting the classical counting inequality for Turán systems. For a $k$-uniform hypergraph with $n$ vertices and $m$ edges, the bound can be evaluated exactly by binary search in time polynomial in the binary lengths of $n$ and $m$. We exhibit separations from the Turán-Spencer and Caro-Tuza bounds for every fixed $k\ge3$, and from the Csaba-Plick--hokoufandeh bound in the $3$-uniform case. For the Caro-Tuza comparison, the separation grows linearly in $k$ on infinitely many regular $k$-uniform hypergraphs.

math.CO↗
arXiv2026

Independence Polynomials of 2-step Nilpotent Lie Algebras

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.

math.RA↗