𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Finite Lattices and Lexicographic Gröbner Bases

✍ Scribed by Annetta Aramova; Jürgen Herzog; Takayuki Hibi


Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
129 KB
Volume
21
Category
Article
ISSN
0195-6698

No coin nor oath required. For personal study only.

✦ Synopsis


By means of combinatorics on finite distributive lattices, lexicographic quadratic Gröbner bases of certain kinds of subrings of an affine semigroup ring arising from a finite distributive lattice will be studied.


📜 SIMILAR VOLUMES


Multiplicative Bases, Gröbner Bases, and
✍ Edward L. Green 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 314 KB

In this paper, we study conditions on algebras with multiplicative bases so that there is a Gröbner basis theory. We introduce right Gröbner bases for a class of modules. We give an elimination theory and intersection theory for right submodules of projective modules in path algebras. Solutions to h

Counting and Gröbner Bases
✍ K. Kalorkoti 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 239 KB

We show how the complexity of counting relates to the well known phenomenon that computing Gröbner bases under a lexicographic order is generally harder than total degree orders. We give simple examples of polynomials for which it is very easy to compute their Gröbner basis using a total degree orde

Regular Gröbner Bases
✍ Jonas MÅnsson; Patrik Nordbeck 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 366 KB

In this paper we introduce the concept of bi-automaton algebras, generalizing the automaton algebras previously defined by Ufnarovski. A bi-automaton algebra is a quotient of the free algebra, defined by a binomial ideal admitting a Gröbner basis which can be encoded as a regular set; we call such a

Gröbner Bases Applied to Finitely Genera
✍ Jörn Müller-Quade; Rainer Steinwandt 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 442 KB

Using a constructive field-ideal correspondence it is shown how to compute the transcendence degree and a (separating) transcendence basis of finitely generated field extensions k( x)/k( g), resp. how to determine the (separable) degree if k( x)/k( g) is algebraic. Moreover, this correspondence is u

Reduced Gröbner Bases Under Composition
✍ J. Gutierrez; R.R. San Miguel 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 463 KB

In this paper we contribute with one main result to the interesting problem initiated by Hong (1998, J. Symb. Comput. 25, 643-663) on the behaviour of Gröbner bases under composition of polynomials. Polynomial composition is the operation of replacing the variables of a polynomial with other polynom

Taylor and Lyubeznik Resolutions via Grö
✍ Werner M. Seiler 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 286 KB

Taylor presented an explicit resolution for arbitrary monomial ideals. Later, Lyubeznik found that a subcomplex already defines a resolution. We show that the Taylor resolution may be obtained by repeated application of the Schreyer Theorem from the theory of Gröbner bases, whereas the Lyubeznik res