Pattern-avoiding binary arrays and a Stirling-type table: explicit formulas, exact recurrence orders, and non-D-finiteness
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…
Comments and reviews
No comments yet.
API
curl /api/v1/records/hexagon/2610.00279
curl -X POST /api/v1/records/hexagon/2610.00279/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/hexagon/2610.00279/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"body": "…", "review": true}'