The main purpose of this book is to introduce algebraic, combinatorial, and computational
methods to study monomial algebras and their presentation ideals, including Stanley …

Siphons in a chemical reaction system are subsets of the species that have the potential of
being absent in a steady state. We present a characterization of minimal siphons in terms of …

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 …

The toric fiber product is a general procedure for gluing two ideals, homogeneous with
respect to the same multigrading, to produce a new homogeneous ideal. Toric fiber products …

Primary decomposition of commutative monoid congruences is insensitive to certain
features of primary decomposition in commutative rings. These features are captured by the …

We introduce a novel representation of structured polynomial ideals, which we refer to as
chordal networks. The sparsity structure of a polynomial system is often described by a …

Parity binomial edge ideals of simple undirected graphs are introduced. Unlike binomial
edge ideals, they do not have square-free Gröbner bases and are radical if and only if the …

Abstract The Macaulay2 package Binomials contains implementations of specialized
algorithms for binomial ideals, including primary decomposition into binomial ideals. The …

This paper investigates maximizers of the information divergence from an exponential family
\calE. It is shown that the rI-projection of a maximizer P to \calE is a convex combination of P …

We consider the problem of testing whether the points in a complex or real variety with non-
zero coordinates form a multiplicative group or, more generally, a coset of a multiplicative …