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 …

How does an algebraic geometer studying secant varieties further the understanding of
hypothesis tests in statistics? Why would a statistician working on factor analysis raise open …

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

We introduce and study the toric fiber product of two ideals in polynomial rings that are
homogeneous with respect to the same multigrading. Under the assumption that the set of …

We show that the complexity of the Markov bases of multidimensional tables stabilizes
eventually if a single table dimension is allowed to vary. In particular, if this table dimension …

With any finite graph G=(V, E) we associate a projective toric variety XG over a field K as
follows. The coordinates qA| B of the ambient projective space are indexed by unordered …

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 …

We determine the maximal gap between the optimal values of an integer program and its
linear programming relaxation, where the matrix and cost function are fixed but the right …

Associated to any hypergraph is a toric ideal encoding the algebraic relations among its
edges. We study these ideals and the combinatorics of their minimal generators, and derive …

In this paper we prove a conjecture of Sturmfels and Sullivant [12] about toric ideals used in
algebraic statistics. A new connection between commutative algebra and statistics was …