AI Article Synopsis
- The paper investigates the number of -tuples in the symmetric group with commuting components and establishes asymptotic formulas related to this count.
- It also presents general criteria for log-concavity, which can be applied to various cases including the symmetric group.
- Furthermore, the authors derive a theorem similar to Bessenrodt-Ono, providing an inequality that applies to specific families of sequences.
Article Abstract
Denote by the number of -tuples of elements in the symmetric group with commuting components, normalized by the order of . In this paper, we prove asymptotic formulas for . In addition, general criteria for log-concavity are shown, which can be applied to among other examples. Moreover, we obtain a Bessenrodt-Ono type theorem which gives an inequality of the form for certain families of sequences ().
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Source |
|---|---|
| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC11449981 | PMC |
| http://dx.doi.org/10.1007/s40993-024-00562-1 | DOI Listing |
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