Proof of the Refined Alternating Sign Matrix Conjecture
| dc.creator | Zeilberger, Doron | |
| dc.date | 1996-06-03 | |
| dc.date.accessioned | 2026-07-07T09:15:34Z | |
| dc.date.available | 2026-07-07T09:15:34Z | |
| dc.description | Mills, Robbins, and Rumsey conjectured, and Zeilberger proved, that the number of alternating sign matrices of order $n$ equals $A(n):={{1!4!7! ... (3n-2)!} \over {n!(n+1)! ... (2n-1)!}}$. Mills, Robbins, and Rumsey also made the stronger conjecture that the number of such matrices whose (unique) `1' of the first row is at the $r^{th}$ column, equals $A(n) {{n+r-2} \choose {n-1}}{{2n-1-r} \choose {n-1}}/ {{3n-2} \choose {n-1}}$. Standing on the shoulders of A.G. Izergin, V. E. Korepin, and G. Kuperberg, and using in addition orthogonal polynomials and $q$-calculus, this stronger conjecture is proved. | |
| dc.description | Plain TeX | |
| dc.identifier | https://arxiv.org/abs/math/9606224 | |
| dc.identifier | http://arxiv.org/abs/math/9606224 | |
| dc.identifier | New York J. Math 2(1996), 59-68 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/153059 | |
| dc.subject | Combinatorics | |
| dc.title | Proof of the Refined Alternating Sign Matrix Conjecture | |
| dc.type | text |