Generators of truncated symmetric polynomials

TL;DR

This paper studies the ideal of truncated symmetric polynomials, providing a generating set in arbitrary positive characteristic and proposing a conjecture for minimal generators, advancing understanding of permutation invariants in algebraic topology.

Contribution

It extends the description of generators of truncated symmetric polynomial ideals to arbitrary positive characteristic and introduces a conjecture for their minimal generating sets.

Findings

Provided a generating set for the ideal in arbitrary positive characteristic

Proposed a conjecture for the minimal generators of the ideal

Enhanced understanding of permutation invariant subrings in cohomology

Abstract

Adem and Reichstein introduced the ideal of truncated symmetric polynomials to present the permutation invariant subring in the cohomology of a finite product of projective spaces. Building upon their work, I describe a generating set of the ideal of truncated symmetric polynomials in arbitrary positive characteristic, and offer a conjecture for minimal generators.