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New permanent approximation inequalities via identities

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Abstract

The aim of this paper is to present newupper bounds for the distance between a properly normalized permanent of a rectangular complex matrix and the product of the arithmetic means of the entries of its columns. It turns out that the bounds improve those from earlier work. Our proofs are based on some new identities for the above-mentioned difference and also for related expressions for matrices over a rational associative commutative unital algebra. Some of our identities are generalizations of results in [J. Dougall, Quantitative proofs of certain algebraic inequalities, Proc. Edinb. Math. Soc., 24:61–77, 1905]. Second-order results are also included.

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  1. FB IV – Department of Mathematics, University of Trier, 54286, Trier, Germany

    Bero Roos

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Roos, B. New permanent approximation inequalities via identities. Lith Math J 60, 248–275 (2020). https://doi.org/10.1007/s10986-020-09475-9

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  • DOI: https://doi.org/10.1007/s10986-020-09475-9

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