Abstract

A Hankel matrix (or persymmetric matrix) is a matrix (a ij ) in which for every r the entries on the diagonal i + j = r are the same, i.e., a i,r-i = c r for some c r . For a sequence c 0 , c 1 , c 2 , . . . of real numbers we consider the collection of Hankel matrices n , k = 0, 1, . . ., n = 1, 2, . . ., where # # # # # . . . . . . . . . . . . # # # # # . (1) So the parameter n denotes the size of the matrix and the 2n 1 successive elements c k , c k+1 , . . . , c k+2n-2 occur in the diagonals of the Hankel matrix. We shall further denote the determinant of a Hankel matrix by n ). Hankel matrices occur in the Berlekamp - Massey algorithm for the decoding of BCH - codes and they found recent applications in Combinatorics motivated by the proof of the refined alternating sign matrix conjecture on the one hand and by the derivation of combinatorial identities for their determinants on the other hand. One such identity concerns the Catalan numbers

Citations