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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…
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…