## Integral monoid duality models |

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### Contents

THE XFDDUALITY MODEL | 13 |

LINEAR NONNEGATIVE INTEGRAL DUALITIES | 39 |

A SUPERADDITIVE NONNEGATIVE INTEGRAL DUALITY | 49 |

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### Common terms and phrases

Chapter Chvatal functions coefficients cone duality cone(Y conv(S convex hull Corollary defined Definition denotes elimination scheme equivalent f E C Farkas property Farkas's Lemma feasible solutions finite number finite set finitely constrained set finitely generated integral finitely generated set following proposition Fourier-Motzkin elimination function f G Zn Hence Hilbert Basis Theorem induction integer programming problem integral monoid integral vectors Let f linear functions linear programming problem matrix A E Minkowski Minkowski's Theorem nonempty nonnegative integral duality nonnegative rational combinations polyhedron positive integer pre-rank Proof property holds result rows Section set in Xn set of functions set of integral simplex algorithm slice standard constraints standard homogenization subspace superadditive functions suppose valid inequality Weyl Weyl's Theorem x E Zn X-constrained X-Farkas X-Fulkerson X-Minkowski property X-Weyl property X,F,D)-duality Y C Xn Z-module Zariski topology Zmxn