Gröbner Bases of Nested Configurations
نویسندگان
چکیده
In this paper we introduce a new and large family of configurations whose toric ideals possess quadratic Gröbner bases. As an application, a generalization of algebras of Segre–Veronese type will be studied.
منابع مشابه
Gröbner bases of contraction ideals
We investigate Gröbner bases of contraction ideals under monomial homomorphisms. As an application, we generalize the result of Aoki–Hibi–Ohsugi– Takemura and Ohsugi–Hibi for toric ideals of nested configurations.
متن کاملSupernormal Vector Configurations
A configuration of lattice vectors is supernormal if it contains a Hilbert basis for every cone spanned by a subset. We study such configurations from various perspectives, including triangulations, integer programming and Gröbner bases. Our main result is a bijection between virtual chambers of the configuration and virtual initial ideals of the associated binomial ideal.
متن کاملPolynomial ideals for sandpiles and their Gröbner bases
A polynomial ideal encoding topplings in the abelian sandpile model on a graph is introduced. A Gröbner basis of this ideal is interpreted combinatorially in terms of well-connected subgraphs. This gives rise to algorithms to determine the identity and the operation in the group of recurrent configurations.
متن کاملComprehensive Gröbner bases and von Neumann regular rings
There is a close relation between comprehensive Gröbner bases and non-parametric Gröbner bases over commutative von Neumann regular rings. By this relation, Gröbner bases over a commutative von Neumann regular ring can be viewed as an alternative to comprehensive Gröbner bases. (Therefore, this Gröbner basis is called an “alternative comprehensive Gröbner basis (ACGB)”.) In the first part of th...
متن کاملDirect Solution of the 7 parameters transformation problem
In this paper, we propose a new algorithm to solve the 7 parameters transformation problem. Using Gröbner bases techniques and solving polynomial systems, we find, in a direct manner and without the need of a linearization, the values of the translation, rotation and a scale factor. Then, with the aid of simulated data, we will confront the algorithm to all sorts of configurations. Finally, we ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008