Symmetry in maximal (s-1,s+1) cores

2014/11/03 by Rishi Nath, Nath, Rishi
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1411.0339

arxiv created 2014/11/03 · openalex publication_date 2014/11/03 · arxiv updated 2014/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We explain a "curious symmetry" for maximal (s-1,s+1)-core partitions first observed by T. Amdeberhan and E. Leven. Specifically, using the s-abacus, we show such partitions have empty s-core and that their s-quotient is comprised of 2-cores. This imposes strong conditions on the partition structure, and implies both the Amdeberhan-Leven result and additional symmetry. We also find a more general family that exhibits these symmetries.

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