Indispensable monomials of toric ideals and Markov bases

Extending the notion of indispensable binomials of a toric ideal ((14), (7)), 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 binomials generators of a toric ideal. Some examples of indispensable monomials from statistical models for contingency tables are given.

• Type: Journal
• Year: 2008
• Where: JSC
• Authors: Satoshi Aoki, Akimichi Takemura, Ruriko Yoshida
• Keywords: Indispensable Binomials, Indispensable Monomials, JSC 2008, Toric Ideal