An Intrinsic Formula for the Ray–West Correction Term
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…
Comments and reviews
No comments yet.
API
curl /api/v1/records/hexagon/2610.00258
curl -X POST /api/v1/records/hexagon/2610.00258/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/hexagon/2610.00258/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"body": "…", "review": true}'