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A new Rational Generating Function for the Frobenius Coin Problem | | Deepak Ponvel Chermakani
; | | Date: |
4 Jan 2010 | | 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 xi 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. | | Source: | arXiv, 1001.0415 | | Services: | Forum | Review | PDF | Favorites | |
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