18 citations · 42 across the 18 of their papers we have counts for
10 papers · 1 filter
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…
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…
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 minima…
SubalgebraBases in Macaulay2
Michael Burr, Oliver Clarke, Timothy Duff +3
We describe a recently revived version of the software package SubalgberaBases, which is distributed in the Macaulay2 computer algebra system. The package allows the user to comput…
Standard monomial theory and toric degenerations of Richardson varieties in the Grassmannian
Narasimha Chary Bonala, Oliver Clarke, Fatemeh Mohammadi
Richardson varieties are obtained as intersections of Schubert and opposite Schubert varieties. We provide a new family of toric degenerations of Richardson varieties inside Grassm…
Conditional probabilities via line arrangements and point configurations
Oliver Clarke, Fatemeh Mohammadi, Harshit J. Motwani
We study the connection between probability distributions satisfying certain conditional independence (CI) constraints, and point and line arrangements in incidence geometry. To a…
Standard monomial theory and toric degenerations of Schubert varieties from matching field tableaux
Oliver Clarke, Fatemeh Mohammadi
We study Gröbner degenerations of Schubert varieties inside flag varieties. We consider toric degenerations of flag varieties induced by matching fields and semi-standard Young tab…
Toric degenerations of flag varieties from matching field tableaux
Oliver Clarke, Fatemeh Mohammadi
We present families of tableaux which interpolate between the classical semi-standard Young tableaux and matching field tableaux. Algebraically, this corresponds to SAGBI bases of…
Toric degenerations of Grassmannians and Schubert varieties from matching field tableaux
Oliver Clarke, Fatemeh Mohammadi
We study the combinatorics of Gröbner degenerations of Grassmannians and the Schubert varieties inside them. We provide a family of binomial ideals whose combinatorics is governed…
Conditional independence ideals with hidden variables
Oliver Clarke, Fatemeh Mohammadi, Johannes Rauh
We study a class of determinantal ideals that are related to conditional independence (CI) statements with hidden variables. Such CI statements correspond to determinantal conditio…