Frobenius Coin-Exchange Generating Functions
نویسندگان
چکیده
منابع مشابه
A new Rational Generating Function for the Frobenius Coin Problem
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 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 Recurrenc...
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Given a set of positive integers A = {a1, . . . , ad} with gcd(a1, . . . , ad) = 1, we call an integer n representable if there exist nonnegative integers m1, . . . ,md such that n = m1a1 + · · ·+mdad . In this paper, we discuss the linear diophantine problem of Frobenius: namely, find the largest integer which is not representable. We call this largest integer the Frobenius number g(a1, . . . ...
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In its simplest form, the coin problem is this: what is the largest positive amount of money that cannot be obtained using two coins of specified distinct denominations? For example, using coins of 2 units and 3 units, it is easy so see that every amount greater than or equal to 2 can be obtained, but 1 cannot be obtained. Using coins of 2 units and 5 units, every amount greater than or equal t...
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Generalized Frobenius partitions, or F -partitions, have recently played an important role in several combinatorial investigations of basic hypergeometric series identities. The goal of this paper is to use the framework of these investigations to interpret families of infinite products as generating functions for F -partitions. We employ q-series identities and bijective combinatorics.
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ژورنال
عنوان ژورنال: The American Mathematical Monthly
سال: 2020
ISSN: 0002-9890,1930-0972
DOI: 10.1080/00029890.2020.1707625