2012•arXiv (Cornell University)Open access

On permanents of matrices over a commutative additively idempotent semiring

Yan Huang, Haifeng Lian

Abstract

Let $R$ be a commutative additively idempotent semiring. In this paper, some properties and characterizations for permanents of matrices over $R$ are established, and several inequalities for permanents are given. Also, the adjiont matrices of matriecs over $R$ are considered. Partial results obtained in this paper generalize the corresponding ones on fuzzy matrices, on lattice matrices and on incline matrices.

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Key concepts: Semiring, Idempotence, Mathematics, Commutative property, Idempotent matrix, Pure mathematics, Combinatorics, Algebra over a field