28 citations · 81 across the 14 of their papers we have counts for
23 papers
Faithful linear and relational representations of diagram categories and monoids
James East, Marianne Johnson, Mark Kambites
We study representations of diagram categories by binary relations and matrices over rings and semirings. Our main result is a faithful involutive tensor representation of the part…
Semirings of formal sums and injective partial transformations
Maximilien Gadouleau, Marianne Johnson
The semiring of discrete dynamical systems is a simple algebraic model for modularity in deterministic systems. The objects of the semiring are finite transformations (viewed as di…
The structure of End()
Victoria Gould, Ambroise Grau, Marianne Johnson
The full transformation semigroups , where , consisting of all maps from a set of cardinality to itself, are arguably the most important family…
Representations and identities of plactic-like monoids
Alan J. Cain, Marianne Johnson, Mark Kambites +1
We exhibit faithful representations of the hypoplactic, stalactic, taiga, sylvester, Baxter and right patience sorting monoids of each finite rank as monoids of upper triangular ma…
Linear functions preserving Green's relations over fields
Alexander Guterman, Marianne Johnson, Mark Kambites +1
We study linear functions on the space of matrices over a field which preserve or strongly preserve each of Green's equivalence relations (, …
Matrix semigroups over semirings
Victoria Gould, Marianne Johnson, Munazza Naz
The multiplicative semigroup of matrices over a field is well understood, in particular, it is a regular semigroup. This paper considers semigroups of the…