Proves a local limit theorem for the number of parts in t-regular partitions, indicating convergence rates.
For any integer t ≥ 2 , we prove a local limit theorem (LLT) with an explicit convergence rate for the number of parts in a uniformly chosen t -regular partition. When $t = 2$ , this recovers the LLT for partitions into distinct parts, as previously established in the work of Szekeres [‘Asymptotic distributions of the number and size of parts in unequal partitions’, Bull. Aust. Math. Soc. 36 (1987), 89–97].
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Bhowmik et al. (2025) studied this question.
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