22 citations · 61 across the 12 of their papers we have counts for
14 papers
New bounds on the periodicity transient of the powers of a tropical matrix: using cyclicity and factor rank
Arthur Kennedy-Cochran-Patrick, Glenn Merlet, Thomas Nowak +1
Building on the weak CSR approach developed in a previous paper by Merlet, Nowak and Sergeev, we establish new bounds for the periodicity threshold of the powers of a tropical matr…
Tropical linear representations of the Chinese monoid
Zur Izhakian, Glenn Merlet
We introduce a faithful tropical linear representation of the Chinese monoid, and thus prove that this monoid admits all the semigroup identities satisfied by tropical triangular m…
Semigroup identities of supertropical matrices
Z. Izhakian, G. Merlet
We prove that, for any , the monoid of all supertropical matrices extending tropical matrices satisfies nontrivial semigroup identities. These identities are carrie…
Semigroup identities of tropical matrices through matrix ranks
Zur Izhakian, Glenn Merlet
We prove the conjecture that, for any , the monoid of all tropical matrices satisfies nontrivial semigroup identities. To this end, we prove that the factor rank of…
On the Tightness of Bounds for Transients of Weak CSR Expansions and Periodicity Transients of Critical Rows and Columns of Tropical Matrix Powers
Glenn Merlet, Thomas Nowak, Sergei Sergeev
We study the transients of matrices in max-plus algebra. Our approach is based on the weak CSR expansion. Using this expansion, the transient can be expressed by ,…
Comparison of max-plus automata and joint spectral radius of tropical matrices
Laure Daviaud, Pierre Guillon, Glenn Merlet
Weighted automata over the max-plus semiring S are closely related to finitely generated semigroups of matrices over S. In this paper, we use results in automata theory to study tw…