A directed graph structure of alternating sign matrices

Affine Alternating Sign Matrices

An Alternating sign matrix is a square matrix of 0’s, 1’s, and −1’s in which the sum of the entries in each row or column is 1 and the signs of the nonzero entries in each row or column alternate. This paper attempts to define an analogue to alternating sign matrices which is infinite and periodic. After showing the analogue we define shares desirable cahracteristics with alternating sign matri...

Alternating sign matrices

Symmetric alternating sign matrices

In this note we consider completions of n×n symmetric (0,−1)-matrices to symmetric alternating sign matrices by replacing certain 0s with +1s. In particular, we prove that any n×n symmetric (0,−1)-matrix that can be completed to an alternating sign matrix by replacing some 0s with +1s can be completed to a symmetric alternating sign matrix. Similarly, any n × n symmetric (0,+1)-matrix that can ...

Patterns of alternating sign matrices

Article history: Received 14 April 2011 Accepted 1 March 2012 Available online xxxx Submitted by N. Shaked-Monderer In admiration, to Avi Berman, Moshe Goldberg, and Raphi Loewy AMS classification: 05B20 05C22 05C50 15B36

Alternating sign matrices and tournaments