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On the restricted partition function via determinants with Bernoulli polynomials. II
Volume 61, no. 2
(2020),
pp. 431–440
https://doi.org/10.33044/revuma.v61n2a15
Abstract
Let r≥1 be an integer, a=(a1,…,ar) a vector of positive
integers, and let D≥1 be a common multiple of a1,…,ar. We prove
that if D=1 or D is a prime number then the restricted partition function
pa(n):= the number of integer solutions (x1,…,xr) to ∑rj=1ajxj=n, with x1≥0,…,xr≥0, can be computed by solving a
system of linear equations with coefficients that are values of Bernoulli
polynomials and Bernoulli–Barnes numbers.
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Published by the Unión Matemática Argentina |
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