28 citations · 162 across the 42 of their papers we have counts for
9 papers · 1 filter
Ideals of polynomial semirings in tropical mathematics
Zur Izhakian, Louis Rowen
We describe the ideals, especially the prime ideals, of semirings of polynomials over layered domains, and in particular over supertropical domains. Since there are so many of them…
C-independence and c-rank of posets and lattices
Zur Izhakian, John Rhodes
Continuing with the authors concept (and results) of defining independence for columns of a boolean and superboolean matrix, we apply this theory to finite lattices and finite pose…
Superboolean rank and the size of the largest triangular submatrix of a random matrix
Zur Izhakian, Svante Janson, John Rhodes
We explore the size of the largest (permuted) triangular submatrix of a random matrix, and more precisely its asymptotical behavior as the size of the ambient matrix tends to infin…
Supertropical Monoids: Basics, Canonical Factorization, and Lifting Ghosts to Tangibles
Zur Izhakian, Manfred Knebusch, Louis Rowen
Supertropical monoids are a structure slightly more general than the supertropical semirings, which have been introduced and used by the first and the third authors for refinements…
Boolean Representations of Matroids and Lattices
Zur Izhakian, John Rhodes
We introduce a new representation concept for lattices by boolean matrices, and utilize it to prove that any matroid is boolean representable. We show that such a representation ca…
Pure Dimension and Projectivity of Tropical Polytopes
Zur Izhakian, Marianne Johnson, Mark Kambites
We study how geometric properties of tropical convex sets and polytopes, which are of interest in many application areas, manifest themselves in their algebraic structure as module…