A determinant formula for the partition function p(7k + a)
Jerome Malenfant
TL;DR
This paper presents a novel determinant formula for calculating the partition function p(n) specifically for numbers of the form 7k + a, providing a new mathematical approach to partition theory.
Contribution
It introduces a determinant-based expression for p(7k + a), advancing the analytical tools available for partition functions in number theory.
Findings
Derived explicit determinant formulas for p(7k + a)
Provides a new method for calculating partition functions in specific residue classes
Enhances understanding of partition function structure in modular forms
Abstract
We derive expressions for the partition function p(n), with n in the form 7k+a, as (k+1)-dimensional determinants.
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Taxonomy
TopicsAdvanced Mathematical Identities · Analytic Number Theory Research · Advanced Combinatorial Mathematics