2004/09/01 by Noureddine Chair, Chair, Noureddine
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Number Theory (math.NT) #hep-th #math.NT
paper · pdf · doi:10.48550/arxiv.hep-th/0409011
14 pages
arxiv created 2004/09/01 · arxiv updated 2009/12/01
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, θ4. 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.