On the combinatorics of r-chain minimal and maximal excludants Article Swipe
Subhash Chand Bhoria
,
Pramod Eyyunni
,
Runqiao Li
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2312.02620
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2312.02620
The minimal excludant (mex) of a partition was introduced by Grabner and Knopfmacher under the name `least gap' and was revived by a couple of papers due to Andrews and Newman. It has been widely studied in recent years together with the complementary partition statistic maximal excludant (maex), first introduced by Chern. Among such recent works, the first and second authors along with Maji introduced and studied the $r$-chain minimal excludants (r-chain mex) which led to a new generalization of Euler's classical partition theorem and the sum-of-mex identity of Andrews and Newman. In this paper, we first give combinatorial proofs for these two results on r-chain mex. Then we introduce the r-chain maximal excludants (r-chain maex) and establish the associated identity for the sum of r-chain maex over all partitions, both analytically and combinatorially.
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- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2312.02620
- https://arxiv.org/pdf/2312.02620
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4389421658
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- OpenAlex ID
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https://openalex.org/W4389421658Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2312.02620Digital Object Identifier
- Title
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On the combinatorics of r-chain minimal and maximal excludantsWork title
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2023Year of publication
- Publication date
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2023-12-05Full publication date if available
- Authors
-
Subhash Chand Bhoria, Pramod Eyyunni, Runqiao LiList of authors in order
- Landing page
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https://arxiv.org/abs/2312.02620Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2312.02620Direct link to full text PDF
- Open access
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YesWhether a free full text is available
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/2312.02620Direct OA link when available
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Partition (number theory), Chain (unit), Mathematical proof, Mathematics, Combinatorics, Euler's formula, Generalization, Identity (music), Statistic, Combinatorial proof, Discrete mathematics, Philosophy, Geometry, Physics, Mathematical analysis, Statistics, Astronomy, AestheticsTop concepts (fields/topics) attached by OpenAlex
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10Other works algorithmically related by OpenAlex
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