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...
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| Format: | Journal article |
| Language: | English |
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2012
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| _version_ | 1797069464615780352 |
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| author | Lenz, M |
| author_facet | Lenz, M |
| author_sort | Lenz, M |
| collection | OXFORD |
| description | 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 of linear forms. Its Hilbert series depends only on the matroid structure of X. Via the Tutte polynomial, it is related to various other matroid invariants, e.g.the shelling polynomial and the characteristic polynomial.This work unifies and generalizes results by Ardila and Postnikov on power ideals and by Holtz and Ron, and Holtz etal. on (hierarchical) zonotopal algebra. We also generalize a result on zonotopal Cox modules that were introduced by Sturmfels and Xu. © 2012 Elsevier Ltd. |
| first_indexed | 2024-03-06T22:24:51Z |
| format | Journal article |
| id | oxford-uuid:56518938-80df-4c00-9215-3244ec4eff69 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T22:24:51Z |
| publishDate | 2012 |
| record_format | dspace |
| spelling | oxford-uuid:56518938-80df-4c00-9215-3244ec4eff692022-03-26T16:49:34ZHierarchical zonotopal power idealsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:56518938-80df-4c00-9215-3244ec4eff69EnglishSymplectic Elements at Oxford2012Lenz, MZonotopal 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 of linear forms. Its Hilbert series depends only on the matroid structure of X. Via the Tutte polynomial, it is related to various other matroid invariants, e.g.the shelling polynomial and the characteristic polynomial.This work unifies and generalizes results by Ardila and Postnikov on power ideals and by Holtz and Ron, and Holtz etal. on (hierarchical) zonotopal algebra. We also generalize a result on zonotopal Cox modules that were introduced by Sturmfels and Xu. © 2012 Elsevier Ltd. |
| spellingShingle | Lenz, M Hierarchical zonotopal power ideals |
| title | Hierarchical zonotopal power ideals |
| title_full | Hierarchical zonotopal power ideals |
| title_fullStr | Hierarchical zonotopal power ideals |
| title_full_unstemmed | Hierarchical zonotopal power ideals |
| title_short | Hierarchical zonotopal power ideals |
| title_sort | hierarchical zonotopal power ideals |
| work_keys_str_mv | AT lenzm hierarchicalzonotopalpowerideals |