Abstract
In this chapter we give a short summary of algebraic concepts relevant for understanding the theory of Markov bases. In particular the notions of Gröbner basis and toric ideal are important. This section is intended as a reference of relevant definitions and results.
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Sturmfels, B.: Gröbner Bases and Convex Polytopes. In: University Lecture Series, vol. 8. American Mathematical Society, Providence, RI (1996)
Sundberg, R.: Some results about decomposable (or Markov-type) models for multidimensional contingency tables: Distribution of marginals and partitioning of tests. Scand. J. Statist. 2(2), 71–79 (1975)
Cox, D., Little, J., O’Shea, D.: Ideals, varieties, and algorithms. In: Undergraduate Texts in Mathematics, 3rd edn. Springer, New York (2007)
JST CREST Hibi team: Gröbner Bases, Statistics and Sofstware Systems. Kyoritsu Shuppan, Tokyo (2011). (In Japanese)
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Aoki, S., Hara, H., Takemura, A. (2012). Toric Ideals and Their Gröbner Bases. In: Markov Bases in Algebraic Statistics. Springer Series in Statistics, vol 199. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3719-2_3
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DOI: https://doi.org/10.1007/978-1-4614-3719-2_3
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Print ISBN: 978-1-4614-3718-5
Online ISBN: 978-1-4614-3719-2
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