Toric rings and ideals of nested configurations

Toric Ideals in Algebraic Statistics Toric Ideals in Algebraic Statistics

Toric Ideals in Algebraic Statistics

VAGUE RINGS AND VAGUE IDEALS

In this paper, various elementary properties of vague rings are obtained. Furthermore, the concepts of vague subring, vague ideal, vague prime ideal and vague maximal ideal are introduced, and the validity of some relevant classical results in these settings are investigated.

Separative Ideals of Exchange Rings

Toric Codes and Lattice Ideals

Let X be a complete simplicial toric variety over a finite field Fq with homogeneous coordinate ring S = Fq[x1, . . . , xr] and split torus TX ∼= (Fq). We prove that vanishing ideal of a subset Y of the torus TX is a lattice ideal if and only if Y is a subgroup. We show that these subgroups are exactly those subsets that are parameterized by Laurents monomials. We give an algorithm for determin...

Toric Ideals of Phylogenetic Invariants

Statistical models of evolution are algebraic varieties in the space of joint probability distributions on the leaf colorations of a phylogenetic tree. The phylogenetic invariants of a model are the polynomials which vanish on the variety. Several widely used models for biological sequences have transition matrices that can be diagonalized by means of the Fourier transform of an abelian group. ...