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Toric degenerations of Grassmannians and Schubert varieties from matching field tableaux
Abstract We study Grobner degenerations of Grassmannians and the Schubert varieties inside them. We provide a family of binomial ideals whose combinatorics is governed by matching field tableaux inExpand
Cryptography and Liberty: 'Can the Trusted Third Parties be Trusted ? A Critique of the Recent UK Proposals'
It is argued that key escrow represents an unprecedented intrusion on individual privacy, holds back the development of digital communications and commerce, and does not achieve the government's stated goals of helping to prevent crime. Expand
Standard monomial theory and toric degenerations of Richardson varieties inside Grassmannians and flag varieties
We study toric degenerations of opposite Schubert and Richardson varieties inside degenerations of Grassmannians and flag varieties. These degenerations are parametrized by matching fields in theExpand
Toric degenerations of flag varieties from matching field tableaux
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 Plucker algebras.Expand
Conditional independence ideals with hidden variables
This work studies a class of determinantal ideals that are related to conditional independence (CI) statements with hidden variables, and focuses on an example that generalizes the CI ideals of the intersection axiom. Expand
Conditional probabilities via line arrangements and point configurations
We study the connection between probability distributions satisfying certain conditional independence (CI) constraints, and point and line arrangements in incidence geometry. To a family of CIExpand
Combinatorial mutations and block diagonal polytopes
Matching fields were introduced by Sturmfels and Zelevinsky to study certain Newton polytopes and more recently have been shown to give rise to toric degenerations of various families of varieties.Expand
Matroid stratifications of hypergraph varieties, their realization spaces, and discrete conditional independence models
We study conditional independence (CI) models in statistical theory, in the case of discrete random variables, from the point of view of algebraic geometry and matroid theory. Any CI model withExpand
Standard monomial theory and toric degenerations of Richardson varieties in flag varieties
We study standard monomial bases for Richardson varieties inside the flag variety. In general, writing down a standard monomial basis for a Richardson variety can be challenging, as it involvesExpand