Hardy Ramanujan Journal |

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.

Source : oai:HAL:hal-03208509v1

Volume: Volume 43 - Special Commemorative volume in honour of Srinivasa Ramanujan

Published on: May 6, 2021

Submitted on: April 30, 2021

Keywords: Distribution,Modular forms,Eta-quotients,Integer partition,Minimal excludant,2010 Mathematics Subject Classification. 05A17, 11P83, 11F11, 11F20,[MATH]Mathematics [math]

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