The idea for this book came from the time the authors spent at the Statistics and Applied
Mathematical Sciences Institute (SAMSI) in Research Triangle Park in North Carolina …

Algebraic statistics is a rapidly developing field, where ideas from statistics and algebra
meet and stimulate new research directions. One of the origins of algebraic statistics is the …

In this paper we given some basic characterizations of minimal Markov basis for a
connected Markov chain, which is used for performing exact tests in discrete exponential …

Let $ A=\{\textbf {a} _1,\ldots,\textbf {a} _m\}\subset\mathbb {Z}^ n $ be a vector configuration
and $ I_A\subset K [x_1,\ldots, x_m] $ its corresponding toric ideal. The paper consists of two …

A finitely generated commutative monoid is uniquely presented if it has a unique minimal
presentation. We give necessary and sufficient conditions for finitely generated …

We show how Dickson's lemma yields an algorithm for computing the general N-solution to
a linear system over Z. The method is based in determining several particular solutions. We …

Let S be a cancelative finitely generated commutative semigroup satisfying the property S c3
(-S)=(0)(the last condition will be referred as combinatorially finite in the sequel). Fix a finite …

This work generalises the short resolution given by Pisón Casares ['The short resolution of a
lattice ideal', Proc. Amer. Math. Soc. 131 (4)(2003), 1081–1091] to any affine semigroup. We …

In this paper, we deal with the problem of the uniqueness of a minimal system of binomial
generators of a semigroup ideal. Concretely, we give different necessary and/or sufficient …

This paper is concerned with the combinatorial description of the graded minimal free
resolution of certain monomial algebras which includes toric rings. We explicitly describe …