Proof of the Refined Alternating Sign Matrix Conjecture

dc.creatorZeilberger, Doron
dc.date1996-06-03
dc.date.accessioned2026-07-07T09:15:34Z
dc.date.available2026-07-07T09:15:34Z
dc.descriptionMills, 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.descriptionPlain TeX
dc.identifierhttps://arxiv.org/abs/math/9606224
dc.identifierhttp://arxiv.org/abs/math/9606224
dc.identifierNew York J. Math 2(1996), 59-68
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/153059
dc.subjectCombinatorics
dc.titleProof of the Refined Alternating Sign Matrix Conjecture
dc.typetext

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