منابع مشابه
External zonotopal algebra
We provide a general, unified, framework for external zonotopal algebra. The approach is critically based on employing simultaneously the two dual algebraic constructs and invokes the underlying matroidal and geometric structures in an essential way. This general theory makes zonotopal algebra an applicable tool for a larger class of polytopes.
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...
متن کاملZonotopal Subdivisions of Cyclic Zonotopes
The cyclic zonotope n; d is the zonotope in R d generated by any n distinct vectors of the form 1; t; t 2 ;. .. ; t dÀ1 . It is proved that the re¢nement poset of all proper zonotopal subdivisions of n; d which are induced by the canonical projection p: n; d H 3 n; d, in the sense of Billera and Sturmfels, is homotopy equivalent to a sphere and that any zonotopal subdivision of ...
متن کاملHierarchical 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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra and Its Applications
سال: 2013
ISSN: 0219-4988,1793-6829
DOI: 10.1142/s0219498813500977