Minimal excludant over partitions into distinct parts
Number Theory
2022-04-12 v2 Combinatorics
Abstract
The average size of the "smallest gap" of a partition was studied by Grabner and Knopfmacher in 2006. Recently, Andrews and Newman, motivated by the work of Fraenkel and Peled, studied the concept of the "smallest gap" under the name "minimal excludant" of a partition and rediscovered a result of Grabner and Knopfmacher. In the present paper, we study the sum of the minimal excludants over partitions into distinct parts, and interestingly we observe that it has a nice connection with Ramanujan's function . As an application, we derive a stronger version of a result of Uncu.
Keywords
Cite
@article{arxiv.2105.13875,
title = {Minimal excludant over partitions into distinct parts},
author = {Prabh Simrat Kaur and Subhash Chand Bhoria and Pramod Eyyunni and Bibekananda Maji},
journal= {arXiv preprint arXiv:2105.13875},
year = {2022}
}
Comments
We have added a new proposition in Section 3