Proof of the plethystic Murnaghan-Nakayama rule using Loehr's labelled abacus

Pavel Turek

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arXiv · 2312.02958

Proof of the plethystic Murnaghan-Nakayama rule using Loehr's labelled abacus

Pavel Turek

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Abstract

The plethystic Murnaghan-Nakayama rule describes how to decompose the product of a Schur function and a plethysm of the form $p_r\circ h_m$ as a sum of Schur functions. We provide a short, entirely combinatorial proof of this rule using the labelled abaci introduced in Nicholas A. Loehr. Abacus proofs of Schur function identities. In: SIAM J. Discrete Math. 24.4 (2010), pp. 1356-1370.

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BibTeX RIS

Pavel Turek. 2025-08-13. Proof of the plethystic Murnaghan-Nakayama rule using Loehr's labelled abacus. https://arxiv.org/abs/2312.02958

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