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arXiv · 1304.4257

Markov bases and generalized Lawrence liftings

Hara Charalambous·Apostolos Thoma·Marius Vladoiu
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Abstract

Minimal Markov bases of configurations of integer vectors correspond to minimal binomial generating sets of the assocciated lattice ideal. We give necessary and sufficient conditions for the elements of a minimal Markov basis to be (a) inside the universal Gr{\" o}bner basis and (b) inside the Graver basis. We study properties of Markov bases of generalized Lawrence liftings for arbitrary matrices $A\in\mathcal{M}_{m\times n}(\Bbb{Z})$ and $B\in\mathcal{M}_{p\times n}(\Bbb{Z})$ and show that in cases of interest the {\em complexity} of any two Markov bases is the same.

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BibTeXRIS

Hara Charalambous, Apostolos Thoma, Marius Vladoiu. 2013-04-15. Markov bases and generalized Lawrence liftings. https://arxiv.org/abs/1304.4257

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