On the restricted partition function

Abstract

For a vector $\mathbf{a}=(a_1,\dots ,a_r)$ of positive integers we prove formulas for the restricted partition function $p_{\mathbf{a}}(n):=$ the number of integer solutions $(x_1,\dots ,x_r)$ to ${\sum }_{j=1}^r{a}_j{x}_j=n$ with $x_1\ge 0,\dots ,x_r\ge 0$ and its polynomial part.

arXiv comment21 pages, to appear in The Ramanujan Journal

References in corpus (1)

• Formulae for the number of partitions of n into at most m parts (using the quasi-polynomial ansatz)

Cited by in corpus (3)

• On the restricted partition function via determinants with Bernoulli polynomials
• Three Simple Reduction Formulas for the Denumerant Functions
• On the number of $k$-compositions of $n$ satisfying certain coprimality conditions