3 papers
math.AC2026
Distance Reduction in Bouquet Decompositions and Toric Ideals of Graphs
Oliver Clarke, Dimitra Kosta, Alexander Milner
The distance-reduction property for a generating set, i.e., a Markov basis, of a toric ideal is a condition that ensures tight connectivity of its fibres. In this paper, we study t…
math.AC2025
Computing all minimal Markov bases in Macaulay2
Oliver Clarke, Alexander Milner
We introduce the package allMarkovBases for Macaulay2, which is used to compute all minimal Markov bases of a given toric ideal. The package builds on functionality of 4ti2 by prod…
math.AC2025
Minimal cellular resolutions of powers of matching field ideals
Oliver Clarke, Fatemeh Mohammadi
We study a family of monomial ideals, called block diagonal matching field ideals, which arise as monomial Gröbner degenerations of determinantal ideals. Our focus is on the minim…