Work

Residue class biases in unrestricted partitions, partitions into distinct parts, and overpartitions

Year: 2025

Type: article

Abstract: We prove specific biases in the number of occurrences of parts belonging to two different residue classes a and b, modulo a fixed nonnegative integer m, for the sets of unrestricted partitions, partitions into distinct parts, and overpartitions. These biases follow from inequalities for residue-weighted partition functions for the respective sets of partitions. We also establish asymptotic formulas for the numbers of partitions of size n that belong to these sets of partitions and have a symmetric residue class bias (i.e., for $$1\le a 1 ≤ a < m / 2 and $$b=m-a$$ b = m - a ), as n tends to infinity.

Source: Research in the Mathematical Sciences

DOI: 10.1007/s40687-025-00502-0

Authors: Michael J. Schlosser, Nian Hong Zhou

Institutions: University of Vienna, Guangxi Normal University

Language: English

Topic: Advanced Mathematical Identities

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,090

Funders: National Natural Science Foundation of China, Austrian Science Fund, Universität Wien