Ideals, representations and a symmetrised Bernoulli triangle

TL;DR

This paper explores symmetric group representations derived from an ideal in affine space, providing enhanced understanding of a symmetric Bernoulli triangle sequence through graded and representation-theoretic methods.

Contribution

It introduces new symmetric group representations linked to a specific ideal, offering novel insights into the symmetric Bernoulli triangle sequence.

Findings

Representation-theoretic descriptions of the symmetric Bernoulli triangle

Connections between ideals in coordinate rings and combinatorial sequences

Enhanced understanding of symmetric group actions on polynomial ideals

Abstract

We study some representations of symmetric groups arising from a certain ideal in the coordinate ring of affine n-space. Our results give graded and representation-theoretic enhancements of sequence 337 of the Online Encyclopaedia of Integer Sequences, involving a symmetric version of the Bernoulli triangle.