The Frobenius Problem and Maximal Lattice Free Bodies | Zendy

Herbert E. Scarf | Zendy; David Shallcross | Zendy

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The Frobenius Problem and Maximal Lattice Free Bodies

Author(s) -

Herbert E. Scarf,

David Shallcross

Publication year - 1993

Publication title -

mathematics of operations research

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.619

H-Index - 83

eISSN - 1526-5471

pISSN - 0364-765X

DOI - 10.1287/moor.18.3.511

Subject(s) - mathematics , combinatorics , divisor (algebraic geometry) , integer (computer science) , greatest common divisor , lattice (music) , integer lattice , frobenius theorem (differential topology) , discrete mathematics , geometry , half integer , physics , scalar curvature , curvature , quantum mechanics , ricci flat manifold , computer science , acoustics , programming language

Let p = p1, ', pn be a vector of positive integers whose greatest common divisor is unity. The Frobenius problem is to find the largest integer f* which cannot be written as a nonnegative integral combination of the pi. In this note we relate the Frobenius problem to the topic of maximal lattice free bodies and describe an algorithm for n = 3.

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