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arXiv · 2507.14431

Asymptotics for moments of the minimal partition excludant in congruence classes

Shane Chern·Ernest X. W. Xia
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Abstract

The minimal excludant statistic, which denotes the smallest positive integer that is not a part of an integer partition, has received great interest in recent years. In this paper, we move on to the smallest positive integer whose frequency is less than a given number. We establish an asymptotic formula for the moments of such generalized minimal excludants that fall in a specific congruence class. In particular, our estimation reveals that the moments associated with a fixed modulus are asymptotically ``equal''.

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Shane Chern, Ernest X. W. Xia. 2025-07-19. Asymptotics for moments of the minimal partition excludant in congruence classes. https://arxiv.org/abs/2507.14431

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