13 pagesWe prove the conjecture that, for any $n$, the monoid of all $n \times n$ tropical matrices satisfies nontrivial semigroup identities. To this end, we prove that the factor rank of a large enough power of a tropical matrix does not exceed the tropical rank of the original matrix
We study the algebraic structure of the semigroup of all 2x2 tropical matrices under multiplication....
In this paper, an upper bound for the CP-rank of a matrix over a tropical semiring is obtained, acco...
AbstractWe introduce the notion of the tropical matrix pattern, which provides a powerful tool to in...
13 pagesWe prove the conjecture that, for any $n$, the monoid of all $n \times n$ tropical matrices ...
AbstractWe investigate the Kapranov rank functions of tropical matrices for different ground fields....
International audienceA tropical matrix is a matrix defined over the max-plus semiring. For such mat...
We establish necessary and sufficient conditions for a semigroup identity to hold in the monoid of n...
AbstractWe study Green’s J-order and J-equivalence for the semigroup of all n×n matrices over the tr...
structure of the semigroup of n × n tropical matrices and its connection with the geometry of tropic...
Rank of a real matrix can be defined in many equivalent way. It is interesting that the rank of a ma...
AbstractWe study the algebraic structure of the semigroup of all 2×2 tropical matrices under multipl...
AbstractThe paper gives a complete description of the subgroups of the semigroup of tropical n-by-n ...
AbstractThe notion of the factor rank of tropical matrices is considered. We construct a linear-time...
We study the algebraic structure of the semigroup of all 2 2 tropical matrices under multiplication...
Zur Izhakian: Research supported by the Alexander von Humboldt Foundation. Marianne Johnson: Researc...
We study the algebraic structure of the semigroup of all 2x2 tropical matrices under multiplication....
In this paper, an upper bound for the CP-rank of a matrix over a tropical semiring is obtained, acco...
AbstractWe introduce the notion of the tropical matrix pattern, which provides a powerful tool to in...
13 pagesWe prove the conjecture that, for any $n$, the monoid of all $n \times n$ tropical matrices ...
AbstractWe investigate the Kapranov rank functions of tropical matrices for different ground fields....
International audienceA tropical matrix is a matrix defined over the max-plus semiring. For such mat...
We establish necessary and sufficient conditions for a semigroup identity to hold in the monoid of n...
AbstractWe study Green’s J-order and J-equivalence for the semigroup of all n×n matrices over the tr...
structure of the semigroup of n × n tropical matrices and its connection with the geometry of tropic...
Rank of a real matrix can be defined in many equivalent way. It is interesting that the rank of a ma...
AbstractWe study the algebraic structure of the semigroup of all 2×2 tropical matrices under multipl...
AbstractThe paper gives a complete description of the subgroups of the semigroup of tropical n-by-n ...
AbstractThe notion of the factor rank of tropical matrices is considered. We construct a linear-time...
We study the algebraic structure of the semigroup of all 2 2 tropical matrices under multiplication...
Zur Izhakian: Research supported by the Alexander von Humboldt Foundation. Marianne Johnson: Researc...
We study the algebraic structure of the semigroup of all 2x2 tropical matrices under multiplication....
In this paper, an upper bound for the CP-rank of a matrix over a tropical semiring is obtained, acco...
AbstractWe introduce the notion of the tropical matrix pattern, which provides a powerful tool to in...
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