Alternating sign matrix

In mathematics, an alternating sign matrix is a square matrix of 0s, 1s, and −1s such that the sum of each row and column is 1 and the nonzero entries in each row and column alternate in sign.

[1] They are also closely related to the six-vertex model with domain wall boundary conditions from statistical mechanics.

They were first defined by William Mills, David Robbins, and Howard Rumsey in the former context.

alternating sign matrices is The first few terms in this sequence for n = 0, 1, 2, 3, … are This theorem was first proved by Doron Zeilberger in 1992.

[2] In 1995, Greg Kuperberg gave a short proof[3] based on the Yang–Baxter equation for the six-vertex model with domain-wall boundary conditions, that uses a determinant calculation due to Anatoli Izergin.