Geodesic
Markov bases of conditional independence models for permutations
Kybernetika, Tome 45 (2009) no. 2, pp. 249-260.

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The L-decomposable and the bi-decomposable models are two families of distributions on the set $S_n$ of all permutations of the first $n$ positive integers. Both of these models are characterized by collections of conditional independence relations. We first compute a Markov basis for the L-decomposable model, then give partial results about the Markov basis of the bi-decomposable model. Using these Markov bases, we show that not all bi-decomposable distributions can be approximated arbitrarily well by strictly positive bi-decomposable distributions.
Classification : 60C05, 60J99, 62E10, 62H05
Keywords: conditional independence; Markov basis; closure of exponential family; permutation; L-decomposable 
@article{KYB_2009__45_2_a3,
     author = {Csisz\'ar, Vill\H{o}},
     title = {Markov bases of conditional independence models for permutations},
     journal = {Kybernetika},
     pages = {249--260},
     publisher = {mathdoc},
     volume = {45},
     number = {2},
     year = {2009},
     mrnumber = {2518150},
     zbl = {1165.62007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2009__45_2_a3/}
}
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Csiszár, Villő. Markov bases of conditional independence models for permutations. Kybernetika, Tome 45 (2009) no. 2, pp. 249-260. http://geodesic.mathdoc.fr/item/KYB_2009__45_2_a3/