Equivariant lattice bases

Lattices and convex bodies in (n) dimensions (aspects of discrete geometry) (52C07) Grassmannians, Schubert varieties, flag manifolds (14M15) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Symmetric groups (20B30) Group actions on combinatorial structures (05E18)

Cites Work

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Markov bases in algebraic statistics.
Finite Gröbner bases in infinite dimensional polynomial rings and applications
A finiteness theorem for Markov bases of hierarchical models
Noetherianity for infinite-dimensional toric varieties
Lectures on algebraic statistics
Finiteness for the \(k\)-factor model and chirality varieties
Higher Lawrence configurations.
Markov bases for decomposable graphical models
A divide-and-conquer algorithm for generating Markov bases of multi-way tables
Algebraic algorithms for sampling from conditional distributions
Gröbner bases of lattices, corner polyhedra, and integer programming
Finiteness theorems and algorithms for permutation invariant chains of Laurent lattice ideals
Equivariant Hilbert series in non-Noetherian polynomial rings
Representation theory and homological stability.
Bounded-rank tensors are defined in bounded degree
Markov bases of three-way tables are arbitrarily complicated
The theory of well-quasi-ordering: a frequently discovered concept
Graph Theory
Equivariant lattice generators and Markov bases
Noetherianity up to Symmetry
Finite generation of symmetric ideals
Polytopes, Rings, and K-Theory
Gröbner Bases for the Polynomial Ring with Infinite Variables and Their Applications
On the foundations of linear and integer linear programming I
Algebraic Statistics
Minimal Basis for a Connected Markov Chain over 3 x 3 x K Contingency Tables with Fixed Two-Dimensional Marginals
Invariant Chains in Algebra and Discrete Geometry
Ordering by Divisibility in Abstract Algebras
Theorems of Carathéodory, Minkowski–Weyl, and Gordan up to Symmetry

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