Partition Identities From Partial Supersymmetry

TL;DR

This paper connects partial supersymmetry in quantum theory to new identities in partition theory, deriving formulas and generating functions that generalize classical results like Euler's theorem.

Contribution

It introduces a novel link between partial supersymmetry and partition identities, deriving explicit formulas and generating functions that extend classical partition theorems.

Findings

Derived Euler theorem in partition theory from partial supersymmetry.

Obtained explicit formulas for graded parafermionic partition functions.

Established a ratio involving Jacobi Theta function and introduced new partition sequences.

Abstract

In the quantum theory, using the notion of partial supersymmetry, in which some, but not all, operators have superpartners we derive the Euler theorem in partition theory. The paraferminic partition function gives another identity in partition theory with restrictions. Also an explicit formula for the graded parafermionic partition function is obtained. It turns out that the ratio of the former partition function to the latter is given in terms of the Jacobi Theta function, $\theta_{4}$. The inverted graded parafermionic partition function is shown to be a generating function of partitions of numbers with restriction that generalizes the Euler generating function and as a result we obtain new sequences of partitions of numbers with given restrictions.