Semigroup identities of supertropical matrices

Z. Izhakian, G. Merlet

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 languageEnglish
PublisherArXiv
Number of pages6
Publication statusSubmitted - 13 Nov 2019

Bibliographical note

The writing of this paper was completed under the auspices of the Resarch in Pairs program of the Mathematisches Forschungsinstitut Oberwolfach, Germany. The authors thank MFO for the excellent working environment.

Keywords

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

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