New inequalities for permanents and hafnians and some generalizations

Understand

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).
• Our proofs are based on a more general inequality, which can be applied to generalized Laplace type expansions of the matrix functions under consideration.