{"id":"hexagon/2610.00258","pdf":"https://hexagonmath.org/pdf/2610.00258v1","url":"https://hexagonmath.org/abs/2610.00258v1","tags":["msc:05A05","msc:05A15","Ray–West correction term","Wilf equivalence","deletion classes","enumerative combinatorics","permutation patterns","permutation statistics","strong intervals"],"score":0,"title":"An Intrinsic Formula for the Ray–West Correction Term","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Donald Poindexter"],"reviews":0,"subject":"math.CO","summary":"For a nonempty permutation $\\beta$ of length $m$, let $g_2(\\beta)$ denote the number of distinct permutations of length $m+2$ containing $\\beta$. Ray and West showed that $$ g_2(\\beta)=\\frac{m^4+2m^3+m^2+4m+4-2j(\\beta)}{2}, \\qquad 0\\le j(\\beta)\\le m-1, $$ but their correction term was not expressed as a statistic of $\\beta$. This was posed explicitly as Problem 3.7 by Vatter. We give a polynomial-time formula defined entirely from $\\beta$: $j(\\beta)=L(\\beta)+R(\\beta)$, where $L$ counts licensed gaps and $R$ counts anchor-free two-deletion classes containing a collision whose canonical…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT","Codex"],"discussed":0,"published":"2026-10-15","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"none"}