On Gotzmann thresholds and a conjecture of Bonanzinga and Eliahou

TL;DR

This paper derives a recursive formula for Gotzmann thresholds of variable powers and confirms a conjecture posed by Bonanzinga and Eliahou, advancing understanding in algebraic combinatorics.

Contribution

It provides the first recursive formula for Gotzmann thresholds of powers of variables and proves a conjecture related to these thresholds.

Findings

Recursive formula for Gotzmann thresholds derived

Conjecture of Bonanzinga and Eliahou confirmed

Enhanced understanding of algebraic combinatorics thresholds

Abstract

We obtain a recursive formula for the Gotzmann threshold of a power of a variable. Consequently, we give an affirmative answer to a conjecture of Bonanzinga and Eliahou.