Charge functions for all dimensional partitions

The charge functions for n n -dimensional partitions are known for n=2,3,4 n = 2 , 3 , 4 in the literature. In a recent work, we gave the expression for arbitrary odd dimension; here we further conjecture a formula for all even-dimensional cases. This conjecture is proved rigorously for 6D, and numerically verified for 8D.

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Journal
SciPost Physics
Published
2026-09-30
DOI
https://doi.org/10.21468/scipostphys.21.3.079
Primary Topic
Advanced Mathematical Identities
Type
article
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Charge functions for all dimensional partitions

Tian-Shun Chen, Hao Feng, Kilar Zhang
SciPost Physics
Advanced Mathematical Identities
article

Charge functions for all dimensional partitions

Tian-Shun Chen, Hao Feng, Kilar Zhang
article en

Abstract

The charge functions for n n -dimensional partitions are known for n=2,3,4 n = 2 , 3 , 4 in the literature. In a recent work, we gave the expression for arbitrary odd dimension; here we further conjecture a formula for all even-dimensional cases. This conjecture is proved rigorously for 6D, and numerically verified for 8D.

SciPost PhysicsVol. 21(3)
Shanghai University (CN), Shanghai Normal University (CN)
Openalex Percentile: Top 90%
Advanced Mathematical Identities
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Charge functions for all dimensional partitions — Tian-Shun Chen, Hao Feng, et al. · SciPost Physics (2026) | TGRS Research Map | TGRS