On the index of reducibility of powers of a standard parameter ideal

TL;DR

This paper investigates the index of reducibility for powers of standard parameter ideals, providing explicit formulas in special cases and applying these results to compute Hilbert polynomials of socle ideals.

Contribution

It introduces an explicit formula for the index of reducibility of powers of standard parameter ideals and applies it to compute associated Hilbert polynomials.

Findings

Explicit formula for the index of reducibility in special cases

Application to Hilbert polynomial computation of socle ideals

Enhanced understanding of the structure of parameter ideals

Abstract

In this paper we study the index of reducibility of powers of a standard parameter ideal. An explicit formula is proved for the extremely case. We apply the main result to compute Hilbert polynomials of socle ideals of standard parameter ideals.