Symbolic powers of monomial ideals and vertex cover algebras

J Herzog, T Hibi, NV Trung - Advances in Mathematics, 2007 - Elsevier
We introduce and study vertex cover algebras of weighted simplicial complexes. These
algebras are special classes of symbolic Rees algebras. We show that symbolic Rees …

Characterizing Translation-Invariant Bell Inequalities using Tropical Algebra and Graph Polytopes

M Hu, E Vallée, T Seynnaeve, P Emonts… - arXiv preprint arXiv …, 2024 - arxiv.org
Nonlocality is one of the key features of quantum physics, which is revealed through the
violation of a Bell inequality. In large multipartite systems, nonlocality characterization …

Multiplicities of classical varieties

J Jeffries, J Montano, M Varbaro - Proceedings of the London …, 2015 - academic.oup.com
The-multiplicity plays an important role in the intersection theory of Stückrad–Vogel cycles,
while recent developments confirm the connections between the-multiplicity and …

Degree and algebraic properties of lattice and matrix ideals

L O'Carroll, F Planas-Vilanova, RH Villarreal - SIAM Journal on Discrete …, 2014 - SIAM
We study the degree of nonhomogeneous lattice ideals over arbitrary fields, and give
formulas to compute the degree in terms of the torsion of certain factor groups of Z^s and in …

Monomial ideals and the computation of multiplicities

D Delfino, A Taylor, WV Vasconcelos… - … ring theory and …, 2017 - taylorfrancis.com
The theory of the integral closure of ideals has resisted direct approaches to some of its
basic questions (membership and completeness tests, and construction). We mainly treat …

Phylogenetic invariants for group-based models

M Donten-Bury, M Michalek - arXiv preprint arXiv:1011.3236, 2010 - arxiv.org
In this paper we investigate properties of algebraic varieties representing group-based
phylogenetic models. We propose a method of generating many phylogenetic invariants. We …

Quantum jumps of normal polytopes

W Bruns, J Gubeladze, M Michałek - Discrete & Computational Geometry, 2016 - Springer
We introduce a partial order on the set of all normal polytopes in\mathbb R^ d R d. This
poset NPol (d) NPol (d) is a natural discrete counterpart of the continuum of convex compact …

An Introduction to the Theory of Linear Integer Arithmetic

D Chistikov - 44th IARCS Annual Conference on Foundations of …, 2024 - drops.dagstuhl.de
Presburger arithmetic, or linear integer arithmetic (LIA), is a logic that allows one to express
linear constraints on integers: equalities, inequalities, and divisibility by nonzero n∈ ℤ. More …

[HTML][HTML] Phylogenetic complexity of the Kimura 3-parameter model

M Michałek, E Ventura - Advances in Mathematics, 2019 - Elsevier
Phylogenetic complexity of the Kimura 3-parameter model - ScienceDirect Skip to main
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Hilbert polynomial of the Kimura 3-parameter model

K Kubjas - arXiv preprint arXiv:1007.3164, 2010 - arxiv.org
Buczy\'{n} ska and Wi\'{s} niewski showed that for the Jukes Cantor binary model of a 3-
valent tree the Hilbert polynomial depends only on the number of leaves of the tree and not …