This page collects some references to works about Markov bases. The selection is a bit arbitrary, and if you feel
that we have missed an important fact or reference, please tell us.

4ti2 team. 4ti2  A software package for algebraic, geometric and
combinatorial problems on linear spaces. Available at www.4ti2.de.
 Most computations of Markov bases are done using 4ti2.

M. Develin, S. Sullivant. Markov Bases of Binary Graph Models. Annals of Combinatorics 7 (2003), 441466.
 It is stated, that a graph model has Markov degree 2 iff its graph is a forest.
 This paper shows that the Markov degree of the graph models of CN and K(2,N) is 4.

P. Diaconis, B. Sturmfels. Algebraic algorithms for sampling from conditional distributions. Annals of
Statistics, 26 (1998), 363397.
 The idea to use Markov bases in statistics was first published here.
 D. Geiger, C. Meek, B. Sturmfels. On the toric algebra of graphical models. Annals of Statistics 34, Nr 3 (2006), 14631492.
 This paper shows that the Markov degree of a graphical model is 2 iff the graph is decomposable.
 S. Hoşten, S. Sullivant. Gröbner bases and polyhedral geometry of reducible and cyclic models. Journal of Combinatorial Theory Ser. A 100 (2002), 277301.
 This paper shows that the Markov degree of a graphical model is 2 iff the graph is decomposable.
 V. Csiszàr. Conditional independencs relations and loglinear models for random matchings. Acta Mathematica Hungarica, online first.
 Ldecomposable and bidecomposable random permutations are discussed.
 J.I. GarcíaGarcía, M.A. MorenoFrías, A. VigneronTenorio. On the decomposable semigroups and their
applications in Algebraic Statistics.
Arxiv 1006.2557v2 (2011).
 This article decides uniqueness of Markov bases for decomposable models.
 Daniel Irving Bernstein and Seth Sullivant. Unimodular binary hierarchical models. Journal of Combinatorial Theory, Series B 123 (2017): 97125.
 This paper shows unimodularity and thus normality and uniqueness of some Markov bases in the database.
 Daniel Irving Bernstein and Christopher O'Neill. Unimodular hierarchical models and their Graver bases. Journal of Algebraic Statistics 8 (2017): 2943.
 This paper shows unimodularity and thus normality and uniqueness of some Markov bases in the database.