When does the set of \((a, b, c)\)-core partitions have a unique maximal element?

zbMath1325.05024arXiv1408.0550MaRDI QIDQ2346470

Amol Aggarwal

Publication date: 2 June 2015

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1408.0550

zbMATH Keywords

Young diagramcore partitionnumerical semigrouphook lengthposet-UMUM-set

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17)

Related Items (7)

Johnson's bijections and their application to counting simultaneous core partitions ⋮ Advances in the Theory of Cores and Simultaneous Core Partitions ⋮ Simultaneous core partitions: parameterizations and sums ⋮ A combinatorial proof of a relationship between maximal \((2k-1,2k+1)\)-cores and \((2k-1,2k,2k+1)\)-cores ⋮ A bijective proof of Amdeberhan's conjecture on the number of \((s, s + 2)\)-core partitions with distinct parts ⋮ Sizes of simultaneous core partitions ⋮ Abaci structures of \((s, ms\pm1)\)-core partitions

Cites Work

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• A bijection between dominant Shi regions and core partitions
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• On simultaneous \(s\)-cores/\(t\)-cores
• Partitions which are simultaneously \(t_1\)- and \(t_2\)-core
• Armstrong's conjecture for \((k, m k + 1)\)-core partitions
• On the enumeration of \((s, s + 1, s + 2)\)-core partitions
• Block inclusions and cores of partitions.
• Average size of a self-conjugate $(s,t)$-core partition
• The Catalan Case of Armstrong's Conjecture on Simultaneous Core Partitions

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