Dyson's crank and the mex of integer partitions

DOI10.1016/j.jcta.2021.105523zbMath1476.05016arXiv2009.10873OpenAlexW3088782732MaRDI QIDQ2237935

James A. Sellers, Brian Hopkins, Dennis W. Stanton

Publication date: 28 October 2021

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.10873

zbMATH Keywords

crankgenerating functionsinteger partitionsFrobenius symbolsmex

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial identities, bijective combinatorics (05A19) Combinatorial aspects of partitions of integers (05A17) Elementary theory of partitions (11P81) Radix representation; digital problems (11A63)

Related Items (12)

Combinatorial perspectives on the Crank and mex partition statistics ⋮ More on Schmidt's partition theorem ⋮ Ramanujan's theta functions and parity of parts and cranks of partitions ⋮ Verification and generation of unrefinable partitions ⋮ Two partition inequalities related to the minimal excludant ⋮ Partition identities related to the minimal excludant ⋮ A refinement of a result of Andrews and Newman on the sum of minimal excludants ⋮ The minimal excludant and Schmidt's partition theorem ⋮ A new generalization of the minimal excludant arising from an analogue of Franklin's identity ⋮ On Blecher and Knopfmacher's fixed points for integer partitions ⋮ A bijective proof of a generalization of the non-negative crank-odd mex identity ⋮ On the maximal part in unrefinable partitions of triangular numbers

Uses Software

• OEIS

Cites Work

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• Concave compositions
• Analysis of some new partition statistics
• Some observations on Dyson's new symmetries of partitions
• Partitions and the minimal excludant
• On partitions classified by smallest missing part
• Partition recurrences
• Turning the Partition Crank
• New Combinatorial Interpretations of Ramanujan's Partition Congruences Mod 5,7 and 11
• Dyson’s crank of a partition
• Ramanujan's congruences and Dyson's crank
• Notes on plane partitions. I

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