A new Rational Generating Function for the Frobenius Coin Problem
Discrete Mathematics
2010-01-08 v2
Abstract
An important question arising from the Frobenius Coin Problem is to decide whether or not a given monetary sum S can be obtained from N coin denominations. We develop a new Generating Function G(x), where the coefficient of x^i is equal to the number of ways in which coins from the given denominations can be arranged as a stack whose total monetary worth is i. We show that the Recurrence Relation for obtaining G(x), is linear, enabling G(x) to be expressed as a rational function, that is, G(x) = P(x)/Q(x), where both P(x) and Q(x) are Polynomials whose degrees are bounded by the largest coin denomination.
Keywords
Cite
@article{arxiv.1001.0415,
title = {A new Rational Generating Function for the Frobenius Coin Problem},
author = {Deepak Ponvel Chermakani},
journal= {arXiv preprint arXiv:1001.0415},
year = {2010}
}
Comments
2 pages, 1 Theorem, I have now enhanced the explanation for Theorem-1