Asymptotics for moments of the minimal partition excludant in congruence classes

2025/07/19 by Chern, Shane, Xia, Ernest X. W. · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2507.14431

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''.

Citations

• On the maximal part in unrefinable partitions of triangular numbers
• Partitions and the Minimal Excludant
• Bisected theta series, least r-gaps in partitions, and polygonal\n numbers

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