Computing generating sets of lattice ideals and Markov bases of lattices
From MaRDI portal
Publication:840713
DOI10.1016/j.jsc.2009.04.006zbMath1200.13048arXivmath/0508359OpenAlexW1989858490MaRDI QIDQ840713
Raymond Hemmecke, Peter N. Malkin
Publication date: 14 September 2009
Published in: Journal of Symbolic Computation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0508359
Integer programming (90C10) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10)
Related Items
A study of a family of monomial ideals, Random sampling in computational algebra: Helly numbers and violator spaces, Toric geometry of cuts and splits, An algorithm for solving parametric integer program, Minimal generating sets of lattice ideals, Heat-bath random walks with Markov bases, Factorizations of the same length in abelian monoids, Lifting Markov bases and higher codimension toric fiber products, Binomial fibers and indispensable binomials, Linear label code of a root lattice using Gröbner bases, \textsc{Sagbi} combinatorics of maximal minors and a \textsc{Sagbi} algorithm, Computing the binomial part of a polynomial ideal, Computing Gröbner bases of pure binomial ideals via submodules of \(\mathbb Z^n\), On decomposable semigroups and applications., Reconstructing biochemical cluster networks, A fast algorithm for computing multiplicative relations between the roots of a generic polynomial, GENERALIZED REDUCTION TO COMPUTE TORIC IDEALS, Support sets in exponential families and oriented matroid theory, Decompositions of binomial ideals, Minimal set of binomial generators for certain Veronese 3-fold projections, Two variations of graph test in double description method, Fibers of multi-way contingency tables given conditionals: relation to marginals, cell bounds and Markov bases
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Decomposition of integer programs and of generating sets
- On an installation of Buchberger's algorithm
- Computing toric ideals
- Variation of cost functions in integer programming
- On the positive sums property and the computation of Graver test sets
- Algebraic algorithms for sampling from conditional distributions
- Gröbner bases of lattices, corner polyhedra, and integer programming
- Efficiently computing minimal sets of critical pairs
- On the foundations of linear and integer linear programming I
- Test sets and inequalities for integer programs
- Toric ideals of homogeneous phylogenetic models
- A Geometric Buchberger Algorithm for Integer Programming
- An Algorithm to Calculate the Kernel of Certain Polynomial Ring Homomorphisms
- Minimal solutions of linear diophantine systems : bounds and algorithms
- GRIN: An implementation of Gröbner bases for integer programming