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arXiv · 2107.04666

Unrefinable partitions into distinct parts in a normalizer chain

Riccardo Aragona·Roberto Civino·Norberto Gavioli·Carlo Maria Scoppola
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Abstract

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.

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Riccardo Aragona, Roberto Civino, Norberto Gavioli, Carlo Maria Scoppola. 2021-07-09. Unrefinable partitions into distinct parts in a normalizer chain. https://doi.org/10.47443/dml.2021.0109

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