Faculty of Economics and Business Administration Publications Database

A Finite Spectral Representation of the Partition Function

Volume: 42
Number: 1
Pages: 29 - 42
Month: January
Link External Source: Online Version
Year: 2017
Keywords: Finite representations of the partition function; Finite representations of the divisor function; Upper Hessenberg matrix; Spectral representation; Matrix function

Finite representations of the partition function in terms of powers and eigenvalues of a sparse upper Hessenberg matrix are established. The trace of this matrix also yields finite representations of the divisor function. Several identities between partition numbers and other quantities such as matrix functions are derived.