Une identit\'e remarquable en th\'eorie des partitions

TL;DR

This paper proves a conjectured identity about partitions related to shifted Jack polynomials using $mbda$-ring techniques, contributing a new proof method and suggesting future research directions.

Contribution

It provides a new proof of a partition identity conjectured in the context of shifted Jack polynomials, employing $mbda$-ring techniques.

Findings

Proved a partition identity conjectured in shifted Jack polynomial studies.

Used $mbda$-ring techniques for the proof.

Suggested the potential for a bijective proof in future work.

Abstract

We prove an identity about partitions, previously conjectured in the study of shifted Jack polynomials (math.CO/9903020). The proof given is using $\lambda$-ring techniques. It would be interesting to obtain a bijective proof.