# Krawtchouk polynomials and quadratic semi-regular sequences

## TL;DR

This paper establishes bounds on the degree of regularity for quadratic polynomial systems using Krawtchouk polynomials, linking algebraic geometry with orthogonal polynomial theory.

## Contribution

It introduces a novel approach to analyze the degree of regularity by interpreting the Hilbert series through Krawtchouk polynomials, providing new theoretical insights.

## Key findings

- Derived bounds for the degree of regularity
- Connected algebraic systems with orthogonal polynomial theory
- Enhanced understanding of semi-regular polynomial systems

## 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.