Lifting Markov bases and higher codimension toric fiber products. (May 2016)

• Record Type: Journal Article
• Authors: Rauh, Johannes; Sullivant, Seth
• Is Part Of: Journal of symbolic computation. Volume 74(2016)
• Page Start: 276
• Page End: 307
• Publication Date: 2016-05
• Subjects: 11P21 -- 13P10 -- 52B20 -- 90C10 -- 13E15; Markov bases -- Toric fiber product -- Lifting -- Gröbner bases; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2015.07.003
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We study how to lift Markov bases and Gröbner bases along linear maps of lattices. We give a lifting algorithm that allows to compute such bases iteratively provided a certain associated semigroup is normal. Our main application is the toric fiber product of toric ideals, where lifting gives Markov bases of the factor ideals that satisfy the compatible projection property. We illustrate the technique by computing Markov bases of various infinite families of hierarchical models. The methodology also implies new finiteness results for iterated toric fiber products.