Matrix factorizations of determinants and permanents

Bounds for permanents of non-negative matrices

“…If A is an n-square matrix and i and j are positive integers, 1 ^ i, j ^ n, 1 (3) and the assertion about equality hold in case n = 2. Assume that they hold for all non-negative (n -l)-square matrices.…”

Structural modelling and analysis of Object Oriented Systems: a graph theoretic system approach

“…In order to describe proper characterisation of the OOS as derived from combinatorial considerations, a permanent matrix P, is proposed (Jurkat and Ryser, 1996). The matrix function/permanent Per(P) of VPSSM -OOS is capable of describing a whole OOS i.e., system graph in a single multinomial equation.…”

Book Review: Permanents

“…A fascinating approach for obtaining upper bounds for permanents of n X n complex matrices was described by Jurkat and Ryser [20]. Given an n X n matrix A they constructed (£i) X (") matrices P t (A% i = 1, ..., n, whose entries are constructed from the entries of row i of A such that the matrix of the right being a 1 X 1 matrix whose unique entry is per A.…”