Work

Hook‐lengths, symplectic/orthogonal contents and Amdeberhan's conjectures

Year: 2025

Type: article

Abstract: The symplectic/orthogonal contents of partitions are related to the dimensions of irreducible representations of symplectic/orthogonal groups. In 2012, motivated by Nekrasov–Okounkov's hook‐length formula and Stanley's hook‐content formula, Amdeberhan proposed several conjectures about infinite product formulas for certain generating functions of hook‐lengths and symplectic/orthogonal contents. Some special cases of his conjectures were recently proved by Amdeberhan, Andrews and Ballantine. In this paper, we prove the general cases of Amdeberhan's conjectures.

Source: Proceedings of the London Mathematical Society

DOI: 10.1112/plms.70026

Author: Chenglang Yang

Institutions: Chinese Academy of Sciences, Wuhan University, Academy of Mathematics and Systems Science

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, China Postdoctoral Science Foundation, National Postdoctoral Program for Innovative Talents

Awards: G335815763, G7910209117, G805256751, G8533620077