An Analytic Formula for Numbers of Restricted Partitions from Conformal Field Theory

Polyakov, D.

Publication date

March 2017

Abstract

We study the correlators of irregular vertex operators in two-dimensional conformal field theory (CFT) in order to propose an exact analytic formula for calculating numbers of partitions, that is: 1) for given $N,k$, finding the total number $\lambda(N|k)$ of length $k$ partitions of $N$: $N=n_1+...+n_k;0<n_1\leq{n_2}...\leq{n_k}$. 2) finding the total number $\lambda(N)=\sum_{k=1}^N\lambda(N|k)$ of partitions of a natural number $N$ We propose an exact analytic expression for $\lambda(N|k)$ by relating two-point short-distance correlation functions of irregular vertex operators in $c=1$ conformal field theory ( the form of the operators is established in this paper): with the first correlator counting the partitions in the upper half-plane...

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An Analytic Formula for Numbers of Restricted Partitions from Conformal Field Theory

Abstract

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An Analytic Formula for Numbers of Restricted Partitions from Conformal Field Theory

Abstract

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