Details:
Title  Enumeration of finite monomial orderings and combinatorics of universal Gr\"obner bases.  Author(s)  D.A. Pavlov, N.N. Vasiliev  Type  Article in Journal  Abstract  The goal of this work is to analyze various classes of finite and total monomial orderings. The concept of monomial ordering plays the key role in the theory of Gröbner bases: every basis is determined by a certain ordering. At the same time, in order to define a Gröbner basis, it is not necessary to know ordering of all monomials. Instead, it is sufficient to know only a finite interval of the given ordering. We consider combinatorics of finite monomial orderings and its relationship with cells of a universal Gröbner basis. For every considered class of orderings (weakly admissible, convex, and admissible), an algorithm for enumerating finite orderings is discussed and combinatorial integer sequences are obtained. An algorithm for computing all minimal finite orderings for an arbitrary Gröbner basis that completely determine this basis is presented. The paper presents also an algorithm for computing an extended universal Gröbner basis for an arbitrary zerodimensional ideal.  ISSN  03617688; 16083261/e 
URL 
link.springer.com/article/10.1134%2FS0361768809020030 
Language  English  Journal  Program. Comput. Softw.  Volume  35  Number  2  Pages  7989  Publisher  Springer US, New York, NY; Pleiades Publishing, New York, NY; MAIK ``Nauka/Interperiodica  Year  2009  Edition  0  Translation 
No  Refereed 
No 
