INEQUALITIES FOR THE Q-PERMANENT - II

For a complex number q, the q-permanent of an n x n complex matrix A = ((a(ij))), written per(q)( A), is defined as [GRAPHICS] where L(n)is the symmetric group of degree n, and l(sigma) the number of inversions of sigma [i.e., the number of pairs i, j such that 1 less than or equ al to i < j less than or equal to n and sigma(i) > sigma(j)]. The func tion is of interest in that it includes both the determinant and the p ermanent as special cases. It is known that if A is positive semidefin ite and if -1 less than or equal to q less than or equal to 1, then pe r(q)(A) greater than or equal to 0. We obtain results for the q-perman ent, a few of which are generalizations of some results of Ando. (C) 1 998 Elsevier Science Inc.