Distribution of generalized mex-related integer partitions
Résumé
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.
Domaines
Mathématiques [math]
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