Year: 2026
Type: preprint
Abstract: In 1982, Chollet conjectured that $\operatorname{per}(A\circ B)\leq \operatorname{per}(A)\operatorname{per}(B)$ for Hermitian positive semidefinite matrices $A,B$, where $\circ$ denotes the Hadamard (entrywise) product. In this paper, we study natural structural classes for which the conjecture holds. We first show that a stronger inequality holds for a broad class of matrices with bipartite support. We then introduce a simple way of joining positive semidefinite matrices and give conditions under which Chollet's inequality is preserved under this operation. For graph Laplacians, this operation corresponds to vertex coalescence and gives larger structured graph families satisfying Chollet's inequality from simpler graph classes.
Source: arXiv (Cornell University)
Authors: Pant, Priyanshu, Singh, Ranveer
Institution: Indian Institute of Technology Indore
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7157229814
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