Semigroup identities of supertropical matrices

Z. Izhakian; G. Merlet

Semigroup identities of supertropical matrices

Research output: Working paper

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Abstract

We prove that, for any $n$, the monoid of all $n \times n$ supertropical matrices extending tropical matrices satisfies nontrivial semigroup identities. These identities are carried over to walks on labeled-weighted digraphs with double arcs.

Original language	English
Publisher	ArXiv
Number of pages	6
Publication status	Submitted - 13 Nov 2019

Keywords

Tropical (max-plus) matrices
supertropical matrices
idempotent semirings
semigroup identities
semigroup representations
weighted diagraphs

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Izhakian_SemigroupIdentitiesofSupertropicalMatrices_PRESubmitted manuscript, 177 KBLicence: Unspecified

https://arxiv.org/abs/1911.05654Licence: Unspecified

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abstract = "We prove that, for any $n$, the monoid of all $n \times n$ supertropical matrices extending tropical matrices satisfies nontrivial semigroup identities. These identities are carried over to walks on labeled-weighted digraphs with double arcs. ",

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KW - supertropical matrices

KW - idempotent semirings

KW - semigroup identities

KW - semigroup representations

KW - weighted diagraphs

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