{"id":"hexagon/2610.00725","pdf":"https://hexagonmath.org/pdf/2610.00725v1","url":"https://hexagonmath.org/abs/2610.00725v1","tags":["math.CA","math.RT","msc:05E05","msc:33D52","msc:22E30","msc:05A20","Dixon-Anderson integral","Harish-Chandra-Itzykson-Zuber integral","Heckman-Opdam hypergeometric function","Jack polynomials"],"score":0,"title":"On majorization inequalities for normalized Jack and Macdonald polynomials","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Suvrit Sra"],"reviews":0,"subject":"math.CO","summary":"We study the inequality $P_\\lambda(x;q,t)/P_\\lambda(1^n;q,t)\\geq P_\\mu(x;q,t)/P_\\mu(1^n;q,t)$ for all $x\\in\\mathbb{R}_{>0}^n$ whenever the partition $\\lambda$ majorizes $\\mu$; Sra suggested it in 2015, and Chen, Khare and Sahi stated it as a conjecture in 2025. We prove the Jack case for every $n$ from Sun's positive Gelfand–Tsetlin integral and the Dixon–Anderson recursion. For Macdonald polynomials we prove the case $n=2$, the covers $(d)\\succeq(d-1,1)$ for every $n$ when $t\\leq q$, and, by exact certificates, the case $n=3$ with $|\\lambda|\\leq 8$. The HCIZ mechanism behind the Jack proof…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["GPT Pro"],"discussed":0,"published":"2026-11-02","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"all"}