New inequalities for permanents and hafnians and some generalizations

Bero Roos

Published 2019-06-14Version 1

We show new upper bounds for permanents and hafnians, which are particularly useful for complex matrices. Multidimensional permanents and hyperhafnians are considered as well. The permanental bounds improve on a Hadamard type inequality of Carlen, Lieb and Loss (2006, Methods and Applications of Analysis 13, 1-17) and Cobos, K\"uhn and Peetre (2006, Integral Equations and Operator Theory 56, 57-70). Further, the main result in Roos (2019, Linear Algebra and its Applications 571, 58-77) is improved. Our proofs are based on a more general inequality, which can be applied to generalized Laplace type expansions of the matrix functions under consideration.