Permutability of Matrices over Bipotent Semirings

Autor: Thomas Aird, Mark Kambites

Publikováno v: Aird, T & Kambites, M 2022, ' Permutability of matrices over bipotent semirings ', Semigroup Forum . https://doi.org/10.1007/s00233-022-10268-4

We study permutability properties of matrix semigroups over commutative bipotent semirings (of which the best-known example is the tropical semiring). We prove that every such semigroup is weakly permutable (a result previous stated in the literature

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9509af72c44869bf93757da43f95efdb
http://arxiv.org/abs/2101.04016

NP-Completeness in the gossip monoid

Autor: Marianne Johnson, Mark Kambites, Peter Fenner

Publikováno v: Fenner, P, Johnson, M & Kambites, M 2018, ' NP-completeness in the gossip monoid ', International Journal of Algebra and Computation . https://doi.org/10.1142/S0218196718500297

Gossip monoids form an algebraic model of networks with exclusive, transient connections in which nodes, when they form a connection, exchange all known information. They also arise naturally in pure mathematics, as the monoids generated by the set o

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7a7d65f44eb5ac28cc272adee2e963a5
https://doi.org/10.1142/s0218196718500297

Identities in upper triangular tropical matrix semigroups and the bicyclic monoid

Autor: Marianne Johnson, Laure Daviaud, Mark Kambites

Publikováno v: Daviaud, L, Johnson, M & Kambites, M 2018, ' IDENTITIES IN UPPER TRIANGULAR TROPICAL MATRIX SEMIGROUPS AND THE BICYCLIC MONOID ', Journal of Algebra, vol. 501, pp. 503-525 . https://doi.org/10.1016/j.jalgebra.2017.12.032

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 whethe

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::18fcf0d0d6e9f8d3faa47dd460b885be
https://doi.org/10.1016/j.jalgebra.2017.12.032

Tropical representations and identities of plactic monoids

Autor: Marianne Johnson, Mark Kambites

Publikováno v: Johnson, M & Kambites, M 2021, ' Tropical representations and identities of plactic monoids ', Transactions of the American Mathematical Society, vol. 374, no. 6, pp. 4423-4447 . https://doi.org/10.1090/tran/8355

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 Izhakian and subsequently studied by several authors. A conseq

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::85ab9fc14c56c0f4f6b33d5fab3df6ef
http://arxiv.org/abs/1906.03991

On cogrowth, amenability and the spectral radius of a random walk on a semigroup

Autor: Mark Kambites, Rob Gray

Publikováno v: Gray, R D & Kambites, M 2018, ' On Cogrowth, Amenability, and the Spectral Radius of a Random Walk on a Semigroup ', International Mathematics Research Notices, vol. 2020, no. 12, pp. 3753–3793 . https://doi.org/10.1093/imrn/rny125

We introduce two natural notions of cogrowth for finitely generated semigroups --- one local and one global --- and study their relationship with amenability and random walks. We establish the minimal and maximal possible values for cogrowth rates, a

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::762cd3970ad377c8b7c57c2150897783
http://arxiv.org/abs/1706.01313