Gröbner Basis Techniques in Algebraic Combinatorics
نویسندگان
چکیده
Gröbner basis techniques in the algebraic study of triangulations of convex polytopes as well as of the number of faces of simplicial complexes will be discussed. Of these two traditional topics in combinatorics, the first will be studied by using initial ideals of toric ideals and the second will be studied by using generic initial ideals of monomial ideals.
منابع مشابه
COMBINATORIAL-ALGEBRAIC TECHNIQUES IN GRÖBNER BASES THEORY by
§ 0. Preliminary notations and main definitions.
متن کاملSome meeting points of Gröbner bases and combinatorics
Let F be a field, V ⊆ Fn be a set of points, and denote by I(V ) the vanishing ideal of V in the polynomial ring F[x1, . . . , xn]. Several interesting algebraic and combinatorial problems can be formulated in terms of some finite V , and then Gröbner bases and standard monomials of I(V ) yield a powerful tool for solving them. We present the Lex Game method, which allows one to efficiently com...
متن کاملMATH536A Paper: Gröbner Bases
An introduction to Gröbner bases and some of their uses in affine algebraic geometry.
متن کاملGeneric Gröbner Bases: Application to the Constructibility of the Set of the Algebraic and Analytic Gröbner Fans
The contribution of this paper lies in two aspects. The first one deals with a natural notion of generic Gröbner (or standard) bases on an irreducible affine scheme for an ideal depending on parameters. This takes place in rings of differential operators and concerns the algebraic and the formal case. This gives a generalization of some results of V. Weispfenning obtained in a commutative and a...
متن کاملEfficient encoding via Gröbner bases and discrete Fourier transforms for several kinds of algebraic codes
Abstract—Novel encoding scheme for algebraic codes, such as codes on algebraic curves, multidimensional cyclic codes, and hyperbolic cascaded Reed–Solomon codes, is proposed with numerical examples. We make use of the 2-dimensional inverse discrete Fourier transform, which generalizes the Mattson–Solomon polynomial for Reed–Solomon codes. We also generalize the workings of the generator polynom...
متن کامل