Two Polynomial Representations of Experimental Design

Two polynomial representations of experimental design

In the context of algebraic statistics an experimental design is described by a set of polynomials called the design ideal. This, in turn, is generated by finite sets of polynomials. Two types of generating sets are mostly used in the literature: Gröbner bases and indicator functions. We briefly describe them both, how they are used in the analysis and planning of a design and how to switch bet...

Two-wavelet constants for square integrable representations of G/H

In this paper we introduce two-wavelet constants for square integrable representations of homogeneous spaces. We establish the orthogonality relations fo...

Polynomial Surface Patch Representations

Uniqueness of Polynomial Canonical Representations

Abstract. Let P (z) and Q(y) be polynomials of the same degree k ≥ 1 in the complex variables z and y, respectively. In this extended abstract we study the non-linear functional equation P (z) = Q(y(z)), where y(z) is restricted to be analytic in a neighborhood of z = 0. We provide sufficient conditions to ensure that all the roots of Q(y) are contained within the range of y(z) as well as to ha...

Equivariant Polynomial Automorphisms of -representations

We show that every equivariant polynomial automorphism of a-representation and of the reduction of an irreducible-representation is a multiple of the identity.