A refinement of a result of Andrews and Newman on the sum of minimal excludants

Bhoria, Subhash Chand; Eyyunni, Pramod; Maji, Bibekananda

doi:10.48550/arxiv.2110.08108

2021

DOI: 10.48550/arxiv.2110.08108

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A refinement of a result of Andrews and Newman on the sum of minimal excludants

Subhash Chand Bhoria¹,

Pramod Eyyunni²,

Bibekananda Maji³

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“…In addition to [3,24] mentioned above and discussed in more detail below, the interested reader will want to look at [7,8,10,11,14,15,25]. There are even very recent results [9,12,26] that build on a preprint version of this current work.…”

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Combinatorial Perspectives on the Crank and Mex Partition Statistics

Hopkins

Sellers²,

Yee³

2022

Electron. J. Combin.

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Several authors have recently considered the smallest positive part missing from an integer partition, known as the minimum excludant or mex. In this work, we revisit and extend connections between Dyson's crank statistic, the mex, and Frobenius symbols, with a focus on combinatorial proof techniques. One highlight is a generating function expression for the number of partitions with a bounded crank that does not include an alternating sum. This leads to a combinatorial interpretation involving types of Durfee rectangles. A recurring combinatorial technique uses sign reversing involutions on certain triples of partitions to establish a result of Fine and other identities.

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mentioning

confidence: 99%

Combinatorial Perspectives on the Crank and Mex Partition Statistics

Hopkins

Sellers²,

Yee³

2022

Electron. J. Combin.

View full text Add to dashboard Cite

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A refinement of a result of Andrews and Newman on the sum of minimal excludants

Cited by 1 publication

References 0 publications

Combinatorial Perspectives on the Crank and Mex Partition Statistics

Combinatorial Perspectives on the Crank and Mex Partition Statistics

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