Hilbert series and Hilbert depth of squarefree Veronese ideals

TL;DR

This paper derives explicit formulas for the Hilbert series and Hilbert depth of squarefree Veronese ideals in polynomial rings, advancing understanding of their algebraic properties.

Contribution

It provides the first explicit formulas for Hilbert series and depth of these ideals, filling a gap in algebraic combinatorics.

Findings

Explicit formulas for Hilbert series of squarefree Veronese ideals

Explicit formulas for Hilbert depth of these ideals

Enhanced understanding of algebraic properties of these ideals

Abstract

In this paper, we obtain explicit formulas for the Hilbert series and Hilbert depth of squarefree Veronese ideals in a standard graded polynomial ring.