Algorithms for noise removal are either complex or ineffective, and the optimal control with
inequality constrains makes the algorithm even more complex. Now the condition is …

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 posed by …

We establish necessary and sufficient conditions for a semigroup identity to hold in the
monoid of n× n upper triangular tropical matrices, in terms of equivalence of certain tropical …

The technology for multiple-noise removal has triggered skyrocketing interest in both
mathematics and engineering, and the tropical algebra has laid the foundation for an …

Full article: Identities of the Semigroup of Upper Triangular Tropical Matrices Skip to Main
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We give a complete description of Green's 𝒟 relation for the multiplicative semigroup of all
n× n tropical matrices. Our main tool is a new variant on the duality between the row and …

We show that the submonoid of all n× n triangular tropical matrices satisfies a nontrivial
semigroup identity and provide a generic construction for classes of such identities. The …

It is shown that the plactic monoid M of rank 3 3 satisfies the identity wvvwvw= wvwvvw
wvvwvw= wvwvvw where v= xyyx xy xyyx v= xyyxxyxyyx and w= xyyx yx xyyx w= xyyxyxxyyx …

A new tropical plactic algebra is introduced in which the Knuth relations are inferred from the
underlying semiring arithmetic, encapsulating the ubiquitous plactic monoid P n. This …

For each positive n, let un≈ vn denote the identity obtained from the Adjan identity
(xy)(yx)(xy)(xy)(yx)≈(xy)(yx)(yx)(xy)(yx) by substituting (xy)→(x1 x2... xn) and (yx)→(xn... x2 …