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Markov Bases and Generalized Lawrence Liftings

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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 Gröbner basis and (b) inside the Graver basis. We study properties of Markov bases of generalized Lawrence liftings for arbitrary matrices \({A \in \mathcal{M}_{m \times n}(\mathbb{Z})}\) and \({B \in \mathcal{M}_{p \times n}(\mathbb{Z})}\) and show that in cases of interest the complexity of any two Markov bases is the same.

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Authors and Affiliations

  1. Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki, 54124, Greece

    Hara Charalambous

  2. Department of Mathematics, University of Ioannina, Ioannina, 45110, Greece

    Apostolos Thoma

  3. Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei 14, Bucharest, RO-010014, Romania

    Marius Vladoiu

Authors
  1. Hara Charalambous
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  2. Apostolos Thoma
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  3. Marius Vladoiu
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Correspondence to Apostolos Thoma.

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Charalambous, H., Thoma, A. & Vladoiu, M. Markov Bases and Generalized Lawrence Liftings. Ann. Comb. 19, 661–669 (2015). https://doi.org/10.1007/s00026-015-0287-4

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  • DOI: https://doi.org/10.1007/s00026-015-0287-4

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