Indispensable monomials of toric ideals and Markov bases

• Autores: Satoshi Aoki, Akimichi Takemura, Ruriko Yoshida
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 43, Nº 6-7, 2008, págs. 490-507
• Idioma: inglés
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• Resumen

  • Extending the notion of indispensable binomials of a toric ideal [Takemura, Akimichi, Aoki, Satoshi, 2004. Some characterizations of minimal Markov basis for sampling from discrete conditional distributions. Ann. Inst. Statist. Math. 56 (1), 1�17; Ohsugi, Hidefumi, Hibi, Takayuki, 2005. Indispensable binomials of finite graphs. J. Algebra Appl. 4 (4), 421�434], we define indispensable monomials of a toric ideal and establish some of their properties. They are useful for searching indispensable binomials of a toric ideal and for proving the existence or non-existence of a unique minimal system of binomial generators of a toric ideal. Some examples of indispensable monomials from statistical models for contingency tables are given.