Journal of Symbolic Computation
Standard bases and geometric invariant theoryI. Initial ideals and state polytopes
Journal of Symbolic Computation
Regular Article: Cutting Corners
Advances in Applied Mathematics - Special issue dedicated to Henry Crapo
Regular Article: The Number of Plane Corner Cuts
Advances in Applied Mathematics - Special issue dedicated to Henry Crapo
Advances in Applied Mathematics
The Hilbert zonotope and a polynomial time algorithm for universal Gröbner bases
Advances in Applied Mathematics
Linear Transformations in Boolean Complexity Theory
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
SINGULAR: a computer algebra system for polynomial computations
ACM Communications in Computer Algebra
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Polynomial models, in statistics, interpolation and other fields, relate an output 驴 to a set of input variables (factors), x驴=驴(x 1,..., x d ), via a polynomial 驴(x 1,...,x d ). The monomials terms in 驴(x) are sometimes referred to as "main effect" terms such as x 1, x 2, ..., or "interactions" such as x 1 x 2, x 1 x 3, ... Two theories are related in this paper. First, when the models are hierarchical, in a well-defined sense, there is an associated monomial ideal generated by monomials not in the model. Second, the so-called "algebraic method in experimental design" generates hierarchical models which are identifiable when observations are interpolated with 驴(x) based at a finite set of points: the design. We study conditions under which ideals associated with hierarchical polynomial models have maximal Betti numbers in the sense of Bigatti (Commun Algebra 21(7):2317---2334, 1993). This can be achieved for certain models which also have minimal average degree in the design theory, namely "corner cut models".