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math.RA2019
Tropical representations and identities of plactic monoids
Marianne Johnson, Mark Kambites
We exhibit a faithful representation of the plactic monoid of every finite rank as a monoid of upper triangular matrices over the tropical semiring. This answers a question first p…
math.RA2019
Free objects in triangular matrix varieties and quiver algebras over semirings
Mark Kambites
We study the free objects in the variety of semigroups and variety of monoids generated by the monoid of all upper triangular matrices over a commutative semiring. We…