Zobrazeno 1 - 10
of 502
pro vyhledávání: '"Clarke, Oliver"'
Autor:
Clarke, Oliver, Kosta, Dimitra
The distance reducing property for Markov bases is an important property that provides a bound on the mixing time of the associated Markov chain. The goal of this project is to understand properties of distance-reducing Markov bases. We explore the d
Externí odkaz:
http://arxiv.org/abs/2406.17730
Autor:
Clarke, Oliver, Mohammadi, Fatemeh
We study a family of monomial ideals, called block diagonal matching field ideals, which arise as monomial Gr\"obner degenerations of determinantal ideals. Our focus is on the minimal free resolutions of these ideals and all of their powers. Initiall
Externí odkaz:
http://arxiv.org/abs/2404.10729
We study point-line configurations through the lens of projective geometry and matroid theory. Our focus is on their realisation spaces, where we introduce the concepts of liftable and quasi-liftable configurations, exploring cases in which an $n$-tu
Externí odkaz:
http://arxiv.org/abs/2402.07737
The main results of this paper establish a partial correspondence between two previously-studied analogues of Groebner bases in the setting of algebras: namely, subalgebra (aka SAGBI) bases for quotients of polynomial rings and Khovanskii bases for v
Externí odkaz:
http://arxiv.org/abs/2402.06057
We study the maximum likelihood (ML) degree of discrete exponential independence models and models defined by the second hypersimplex. For models with two independent variables, we show that the ML degree is an invariant of a matroid associated to th
Externí odkaz:
http://arxiv.org/abs/2312.10010
Autor:
Clarke, Oliver
This article introduces the package MatchingFields for Macaulay2 and highlights some open problems. A matching field is a combinatorial object whose data encodes a candidate toric degeneration of a Grassmannian or partial flag variety of type A. Each
Externí odkaz:
http://arxiv.org/abs/2306.09693
Autor:
Burr, Michael, Clarke, Oliver, Duff, Timothy, Leaman, Jackson, Nichols, Nathan, Walker, Elise
Publikováno v:
J. Softw. Alg. Geom. 14 (2024) 97-109
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 compute and manipulate subagebra bases -- which are also known as SAGBI base
Externí odkaz:
http://arxiv.org/abs/2302.12473
We study restricted chain-order polytopes associated to Young diagrams using combinatorial mutations. These polytopes are obtained by intersecting chain-order polytopes with certain hyperplanes. The family of chain-order polytopes associated to a pos
Externí odkaz:
http://arxiv.org/abs/2211.07995
We study the equivariant Ehrhart theory of families of polytopes that are invariant under a non-trivial action of the group with order two. We study families of polytopes whose equivariant $H^*$-polynomial both succeed and fail to be effective, in pa
Externí odkaz:
http://arxiv.org/abs/2209.00755