{"docId":7425,"paperId":7425,"url":"https:\/\/hrj.episciences.org\/7425","doi":"10.46298\/hrj.2021.7425","journalName":"Hardy-Ramanujan Journal","issn":"","eissn":"2804-7370","volume":[{"vid":438,"name":"Volume 43 - Special Commemorative volume in honour of Srinivasa Ramanujan - 2020"}],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-03208509","repositoryVersion":1,"repositoryLink":"https:\/\/hal.archives-ouvertes.fr\/hal-03208509v1","dateSubmitted":"2021-04-30 14:21:40","dateAccepted":"2021-05-06 14:08:08","datePublished":"2021-05-06 14:08:34","titles":{"en":"Distribution of generalized mex-related integer partitions"},"authors":["Chakraborty, Kalyan","Ray, Chiranjit"],"abstracts":{"en":"The minimal excludant or \"mex\" function for an integer partition \u03c0 of a positive integer n, mex(\u03c0), is the smallest positive integer that is not a part of \u03c0. Andrews and Newman introduced \u03c3mex(n) to be the sum of mex(\u03c0) taken over all partitions \u03c0 of n. Ballantine and Merca generalized this combinatorial interpretation to \u03c3rmex(n), as the sum of least r-gaps in all partitions of n. In this article, we study the arithmetic density of \u03c3_2 mex(n) and \u03c3_3 mex(n) modulo 2^k for any positive integer k."},"keywords":[{"en":"Distribution"},{"en":"Modular forms"},{"en":"Eta-quotients"},{"en":"Integer partition"},{"en":"Minimal excludant"},"2010 Mathematics Subject Classification. 05A17, 11P83, 11F11, 11F20","[MATH]Mathematics [math]"]}