Proof of the Alternating Sign Matrix Conjecture

Details Proof of the Alternating Sign Matrix Conjecture Proof of the Alternating Sign Matrix Conjecture

1994-07-02

arxiv.org/abs/math/9407211v1

Elec. J. Comb. 3(2)(1996), R13

Mathematics

Combinatorics

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Scientific paper

The number of $n \times n$ matrices whose entries are either -1, 0, or 1,
whose row- and column- sums are all 1, and such that in every row and every
column the non-zero entries alternate in sign, is proved to be $[1!4! >...
(3n-2)!]/[n!(n+1)! ... (2n-1)!]$, as conjectured by Mills, Robbins, and Rumsey.

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