Unrefinable partitions into distinct parts in a normalizer chain
| Autor: | Aragona, Riccardo, Civino, Roberto, Gavioli, Norberto, Scoppola, CARLO MARIA |
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| Rok vydání: | 2021 |
| Předmět: |
symmetric group on 2n elements
unrefinable partitions Partitions Partitions unrefinable partitions finite groups normalizers Group Theory (math.GR) 20B30 20B35 20D20 11P81 05A17 minimal excludant finite groups normalizers partitions into distinct parts QA1-939 FOS: Mathematics Mathematics - Combinatorics Discrete Mathematics and Combinatorics Combinatorics (math.CO) Mathematics - Group Theory sylow 2-subgroups Mathematics |
| Zdroj: | Discrete Mathematics Letters, Vol 8, Pp 72-77 (2021) |
| ISSN: | 2664-2557 |
| Popis: | In a recent paper on a study of the Sylow 2-subgroups of the symmetric group with 2^n elements it has been show that the growth of the first (n-2) consecutive indices of a certain normalizer chain is linked to the sequence of partitions of integers into distinct parts. Unrefinable partitions into distinct parts are those in which no part x can be replaced with integers whose sum is x obtaining a new partition into distinct parts. We prove here that the (n-1)-th index of the previously mentioned chain is related to the number of unrefinable partitions into distinct parts satisfying a condition on the minimal excludant. |
| Databáze: | OpenAIRE |
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