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arXiv · 2605.16577

Statistically characterized subgroups related to arithmetic-type sequence of integers

Pratulananda Das·Ayan Ghosh·Tamim Aziz
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Abstract

Very recently, in [Das et al., J. Lond. Math. Soc., 2025], statistically characterized subgroups were studied for certain classes of non-arithmetic sequences. Subsequently, in [Das et al., Bull. Sci. Math., 2025], characterized subgroups were investigated for a class of arithmetic-type sequences that includes both arithmetic sequences and certain non-arithmetic sequences. Motivated by these developments, we study statistically characterized subgroups associated with a broader class of arithmetic-type sequences. In particular, all previously obtained cardinality related observations for statistically characterized subgroups corresponding to arithmetic sequences as well as certain non-arithmetic sequences follow as special cases of our results. Moreover, we show that this broader class exhibits drastically different behavior and differs significantly from the previously studied special cases.

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Pratulananda Das, Ayan Ghosh, Tamim Aziz. 2026-05-15. Statistically characterized subgroups related to arithmetic-type sequence of integers. https://arxiv.org/abs/2605.16577

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