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Distribution of generalized mex-related integer partitions

Abstract : The minimal excludant or "mex" function for an integer partition π of a positive integer n, mex(π), is the smallest positive integer that is not a part of π. Andrews and Newman introduced σmex(n) to be the sum of mex(π) taken over all partitions π of n. Ballantine and Merca generalized this combinatorial interpretation to σrmex(n), as the sum of least r-gaps in all partitions of n. In this article, we study the arithmetic density of σ_2 mex(n) and σ_3 mex(n) modulo 2^k for any positive integer k.
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Submitted on : Monday, April 26, 2021 - 3:51:13 PM
Last modification on : Monday, March 28, 2022 - 8:14:08 AM
Long-term archiving on: : Tuesday, July 27, 2021 - 7:26:00 PM

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Kalyan Chakraborty, Chiranjit Ray. Distribution of generalized mex-related integer partitions. Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 2021, Volume 43 - Special Commemorative volume in honour of Srinivasa Ramanujan - 2020, pp.122-128. ⟨10.46298/hrj.2021.7425⟩. ⟨hal-03208509⟩

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