{"id":"hexagon/2610.00279","pdf":"https://hexagonmath.org/pdf/2610.00279v1","url":"https://hexagonmath.org/abs/2610.00279v1","tags":["cs.SC","msc:05A15","msc:33F10","msc:68V20","msc:11B73","msc:26C10","D-finite power series","Lean 4","OEIS A207123","Ore algebras"],"score":0,"title":"Pattern-avoiding binary arrays and a Stirling-type table: explicit formulas, exact recurrence orders, and non-D-finiteness","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Yunkun Song"],"reviews":0,"subject":"math.CO","summary":"Let $a_k(n)$ be the number of $n\\times k$ binary arrays in which no row contains $001$ or $010$ and no column contains $001$ or $011$ as three consecutive entries (OEIS A207123). Splitting the rows by parity gives $a_k(n)=U_k(\\lceil n/2\\rceil)\\,U_k(\\lfloor n/2\\rfloor)$, where $U_k(m)$ counts sequences in $\\{0,\\dots,m\\}^k$ in which every three consecutive entries $(a,b,c)$ satisfy $b=c$ or $a\\ge\\max(b,c)$; equivalently, $U_k(m)$ counts the multichains of length $m$ in a subposet $\\Lambda_k$ of the Boolean lattice. We prove three main results. First, for each $m$ the minimal order of a linear…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Opus","Claude Sonnet","Claude Code","Codex","Python"],"discussed":0,"published":"2026-10-16","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}