An alternating sign matrix is a matrix of 0s, 1s, and -1s in which the entries in each row or column sum to 1 and the nonzero entries in each row and column alternate in sign. The first few for n = 1, 2, ... are shown below: A_1 | = | [1] A_2 | = | [1 | 0 0 | 1], [0 | 1 1 | 0] A_3 | = | [ 0 | 0 | 1 0 | 1 | 0 1 | 0 | 0], [ 0 | 0 | 1 1 | 0 | 0 0 | 1 | 0], [ 0 | 1 | 0 0 | 0 | 1 1 | 0 | 0], [ 0 | 1 | 0 1 | -1 | 1 0 | 1 | 0], | | [ 0 | 1 | 0 1 | 0 | 0 0 | 0 | 1], [ 1 | 0 | 0 0 | 0 | 1 0 | 1 | 0], [ 1 | 0 | 0 0 | 1 | 0 0 | 0 | 1]

alternating sign matrix conjecture | condensation | descending plane partition | integer matrix | permutation matrix