Work

The Largest Size of $(t,t+d,t+2d)$-Core Partitions

Year: 2025

Type: article

Abstract: In 2007, Olsson and Stanton determined the largest size of $(t_1,t_2)$-core partitions. Inspired by their result, there have been considerable research on the largest size of simultaneous core partitions. In this work, we compute the largest size of $(t,t+d,t+2d)$-core partitions for any coprime positive integers $t$ and $d$. This generalizes the result by Yang, Zhong, and Zhou, who proved the largest size of $(t,t+1,t+2)$-core partitions.

Source: The Electronic Journal of Combinatorics

DOI: 10.37236/13696

Authors: Hyunsoo Cho, Kyeongjun Lee, Hayan Nam

Institutions: Ewha Womans University, Yonsei University, Duksung Women's University

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Research Foundation, National Research Foundation of Korea, Ministry of Science and ICT, South Korea

Awards: G3308718102, G3793286438, G3994818172, G8314522622