Details:
Title  Some combinatorial applications of Gr\"obner bases.  Author(s)  Tamas Meszaros, Lajos Rónyai  Type  Book, Chapter in Book, Conference Proceeding  Abstract  Let 𝔽 be a field, V⊆𝔽n be a (combinatorially interesting) finite set of points. Several important properties of V are reflected by the polynomial functions on V. To study these, one often considers I(V), the vanishing ideal of V in the polynomial ring 𝔽[x1...xn]. Gröbner bases and standard monomials of I(V) appear to be useful in this context, leading to structural results on V.
Here we survey some work of this type. At the end of the paper a new application of this kind is presented: an algebraic characterization of shatteringextremal families and a fast algorithm to recognize them.  Keywords  Gröbner basis, standard monomial, lexicographic order, vanishing ideal, Hilbert function  ISBN  9783642214929/pbk 
URL 
http://link.springer.com/chapter/10.1007%2F9783642214936_4 
Language  English  Pages  6583  Publisher  Berlin: Springer  Year  2015  Edition  0  Translation 
No  Refereed 
No 
