Year: 2026
Type: preprint
Abstract: We prove a permanental analogue of Koteljanskii's inequality. If $A$ is an inverse $M$-matrix that becomes symmetric after a positive diagonal similarity, then $\mathrm{per}(A_{S\cup T})\,\mathrm{per}(A_{S\cap T})\ge\mathrm{per}(A_S)\,\mathrm{per}(A_T)$ for all $S,T\subseteq[n]$, where $A_S$ is the principal submatrix indexed by $S$. The proof expresses permanents as moments of a complex Gaussian vector and uses Ginibre's correlation inequality. Finally, an explicit counterexample shows that symmetry cannot be dropped.
Source: arXiv (Cornell University)
Author: Sra, Suvrit
Institution: Technical University of Munich
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: Alexander von Humboldt-Stiftung
OpenAlex ID: W7215123928