What question did this study set out to answer?

To explore and define the combinatorial properties of a 6-dimensional hyperrectangle, focusing on its spin classification and configuration enumeration.

April 22, 2026Open Access

Combinatorial Properties of the Configuration Structure of the 6-Dimensional Hyperrectangle — Spin Classification, Configuration Enumeration, and Sign Product

Key Points

To explore and define the combinatorial properties of a 6-dimensional hyperrectangle, focusing on its spin classification and configuration enumeration.
Defined a 6-dimensional structure by adding a discrete label axis to a 5-dimensional hyperrectangle.
Derived combinatorial properties including spin classification and configuration enumeration.
Provided an interpretation example related to the Standard Model.
Identified distinct spin classifications within the configuration structure.
Enumerated various configurations of the 6-dimensional hyperrectangle.
Mapped 62 states to interpretations in the Standard Model.

Abstract

This paper defines a 6-dimensional structure obtained by adding a discrete label axis Q to the 5-dimensional hyperrectangle, and derives combinatorial properties from its configuration structure. The main body derives spin classification, configuration enumeration, and the sign product. Section 10 provides an interpretation example mapping to the Standard Model (62 states). v4: Removed §8 (signed area M(σ)) as trivial for SM particles; renumbered sections accordingly.

Combinatorial Properties of the Configuration Structure of the 6-Dimensional Hyperrectangle — Spin Classification, Configuration Enumeration, and Sign Product

Key Points

Abstract

Cite This Study