nLab alternating sign matrix

Definition

A square matrix with integer entries is an alternating sign matrix if all of the following holds

• entries may be $0,1,-1$ only

• the sum of each row and of each column is $1$

• the nonzero entries in each row and each column alternate in sign

Examples

• every permutation matrix

• the following matrix:

  $$\left( \begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 1 &-1 & 1 \\ 0 & 0 & 1 & 0 \end{array} \right)$$

Literature

• Wikipedia: Alternating sign matrix

• David Bressoud, Proofs and confirmations: the story of the Alternating Sign Matrix Conjecture, Cambridge University Press (1999) [doi:10.1017/CBO9780511613449]

category: algebra