Alternating sign matrices
An alternating sign matrix \(A= (A_{ij})_{1\leq i,j\leq n}\) is an \(n\times n\)-matrix with entries \(\{0, 1, -1\}\), such that in each row and in each column the elements equal to 1 and \(-1\) alternate (if you do not consider the zeros) and the sum of the entries of each row and each column is 1. The authors establish a bijection between the set of the alternating sign matrices of type \(n\times n\) and the set of the \(n\times n\) matrices of type \(\mathcal P\). Then they study the symmetries presented by the alternating sign matrices. By generalizing the matrices of type \(\mathcal P\), one can compute the number of matrices having some symmetries and it is sufficient to consider this kind of matrices in coding theory. An application of these matrices to obtain the configurations of paths of length \(n\) is given in the end of the paper, together with computations for some particular cases.
scientific article; zbMATH DE number 773902