منابع مشابه
Hierarchical zonotopal power ideals
Zonotopal algebra deals with ideals and vector spaces of polynomials that are related to several combinatorial and geometric structures defined by a finite sequence of vectors. Given such a sequence X , an integer k ≥ −1 and an upper set in the lattice of flats of the matroid defined by X , we define and study the associated hierarchical zonotopal power ideal. This ideal is generated by powers ...
متن کاملHierarchical Zonotopal Spaces
Zonotopal algebra interweaves algebraic, geometric and combinatorial properties of a given linear map X. Of basic significance in this theory is the fact that the algebraic structures are derived from the geometry (via a nonlinear procedure known as “the least map”), and that the statistics of the algebraic structures (e.g., the Hilbert series of various polynomial ideals) are combinatorial, i....
متن کاملZonotopal algebra
A wealth of geometric and combinatorial properties of a given linear endomorphism X of IR is captured in the study of its associated zonotope Z(X), and, by duality, its associated hyperplane arrangement H(X). This well-known line of study is particularly interesting in case n := rankX ≪ N . We enhance this study to an algebraic level, and associate X with three algebraic structures, referred he...
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We define the notion of a power stable ideal in a polynomial ring R[X] over an integral domain R. It is proved that a maximal ideal χ M in R[X] is power stable if and only if P t is P primary for all t ≥ 1 for the prime ideal P = M ∩ R. Using this we prove that for a Hilbert domain R any radical ideal in R[X] which is a finite intersection G-ideals is power stable. Further, we prove that if R i...
متن کاملPower of Monomial Ideals
1. Preliminaries 3 2. Gröbner Bases 3 2.1. Motivating Problems 3 2.2. Ordering of Monomials 3 2.3. The Division Algorithm in S = k[x1, . . . , xn] 5 2.4. Dickson’s Lemma 7 2.5. Gröbner Bases and the Hilbert Basis Theorem 10 2.6. Some Further Applications of Gröbner bases 18 3. Hilbert Functions 21 3.1. Macaulay’s Theorem 27 3.2. Hilbert Functions of Reduced Standard Graded k-algebras 37 3.3. Hi...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2012
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2012.01.004