Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Identities in Upper Triangular Tropical Matrix Semigroups and the
  Bicyclic Monoid   We establish necessary and sufficient conditions for a semigroup identity to
hold in the monoid of $n\times n$ upper triangular tropical matrices, in terms
of equivalence of certain tropical polynomials. This leads to an algorithm for
checking whether such an identity holds, in time polynomial in the length of
the identity and size of the alphabet. It also allows us to answer a question
of Izhakian and Margolis, by showing that the identities which hold in the
monoid of $2\times 2$ upper triangular tropical matrices are exactly the same
as those which hold in the bicyclic monoid. Our results extend to a broader
class of "chain structured tropical matrix semigroups"; we exhibit a faithful
representation of the free monogenic inverse semigroup within such a semigroup,
which leads also to a representation by $3\times 3$ upper triangular matrix
semigroups, and a new proof of the fact that this semigroup satisfies the same
identities as the bicyclic monoid.

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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: cs
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con