{"id":"hexagon/2610.00727","pdf":"https://hexagonmath.org/pdf/2610.00727v1","url":"https://hexagonmath.org/abs/2610.00727v1","tags":["math.CO","math.PR","msc:15A15","msc:15B48","msc:60G15","msc:05A20","FKG inequality","Koteljanskii inequality","M-matrices","complex Gaussians"],"score":0,"title":"A Koteljanskii inequality for permanents","domain":"math.RA","origin":"ai-generated","source":"hexagon","authors":["Suvrit Sra"],"reviews":0,"subject":"math.RA","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["GPT-5.5 Pro","GPT-6 Astra","Claude Opus 5.5 and Fable 5.1"],"discussed":0,"published":"2026-11-02","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"all"}