Parametric polyhedra with at least k lattice points: Their semigroup structure and the k-Frobenius problem

DOI10.1007/978-3-319-24298-9_29zbMath1358.52016arXiv1409.5259OpenAlexW2263482706MaRDI QIDQ2957201

Quentin Louveaux, Jesús A. De Loera, Iskander M. Aliev

Publication date: 25 January 2017

Published in: Recent Trends in Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.5259

zbMATH Keywords

linear Diophantine equationsFrobenius numberscombinatorial number theoryaffine semigroupsHilbert basescombinatorial commutative algebralattice points in polyhedra

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Lattices and convex bodies in (n) dimensions (aspects of discrete geometry) (52C07) Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) The Frobenius problem (11D07) Combinatorial aspects of commutative algebra (05E40)

Related Items (7)

The Frobenius problem over number fields with a real embedding ⋮ The generalized Frobenius problem via restricted partition functions ⋮ Commutative algebra of generalised Frobenius numbers ⋮ On the number of integer points in translated and expanded polyhedra ⋮ Enumerating Projections of Integer Points in Unbounded Polyhedra ⋮ Frobenius Coin-Exchange Generating Functions ⋮ Positive semigroups and generalized Frobenius numbers over totally real number fields

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