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Lattice translates of a polytope and the Frobenius problem

✍ Scribed by Ravi Kannan


Publisher
Springer-Verlag
Year
1992
Tongue
English
Weight
961 KB
Volume
12
Category
Article
ISSN
0209-9683

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We study the number of lattice points in integer dilates of the rational polytope x k a k 41 ( ) where a 1 ; . . . ; a n are positive integers. This polytope is closely related to the linear Diophantine problem of Frobenius: given relatively prime positive integers a 1 ; . . . ; a n ; find the lar

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Let X k =[a 1 , a 2 , ..., a k ], k>1, be a subset of N such that gcd(X k )=1. We shall say that a natural number n is dependent (on X k ) if there are nonnegative integers x i such that n has a representation n= k i=1 x i a i , else independent. The Frobenius number g(X k ) of X k is the greatest i