Krawtchouk polynomials and quadratic semi-regular sequences

Abstract

We derive lower und upper bounds for the degree of regularity of an overdetermined, zero-dimensional and homogeneous quadratic semi-regular system of polynomial equations. The analysis is based on the interpretation of the associated Hilbert series as the truncation of the generating function of values of a certain family of orthogonal polynomials, the Krawtchouk polynomials.

9 pages, 5 figures; corrected typos, indices, numerical values; added references and clarifications