Year: 2025
Type: book-chapter
Abstract: Recently, many authors have investigated how various partition statistics distribute as the size of the partition grows. In this work, we look at a particular statistic arising from the recent rejuvenation of MacMahon’s partition analysis. More specifically, we compute all the moments of the alternating sum statistic for partitions. We prove these results using the Circle Method. We also propose a general framework for studying further questions of this type that may avoid some of the complications that arise in traditional approaches to the distributions of partition statistics, and we comment on the utility, comparative ease and opportunities to generalize to very broad settings.
Source: The Ramanujan Journal
Authors: William Craig, Runqiao Li
Institutions: United States Naval Academy, Pennsylvania State University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,990
OpenAlex ID: W4415284039