Name
Abstract | ||
|---|---|---|
For a polyhedral subdivision Δ of a region in Euclideand-space, we consider the vector spaceC
k
r
(Δ) consisting of allC
r
piecewise polynomial functions over Δ of degree at mostk. We consider the formal power series ∑
k≥0
dimℝ C
k
r
(Δ)λk and show, under mild conditions on Δ, that this always has the formP(λ)/(1−λ)
d+1, whereP(λ) is a polynomial in λ with integral coefficients which satisfiesP(0)=1,P(1)=f
d (Δ), andP′(1)=(r+1)f
d−1
0
(Δ). We discuss how the polynomialP(λ) and bases for the spacesC
k
r
(Δ) can be effectively calculated by use of Grbner basis techniques of computational commutative algebra. A further application
is given to the theory of hyperplane arrangements. |
Year | DOI | Venue |
|---|---|---|
1991 | 10.1007/BF02574678 | Discrete & Computational Geometry |
Keywords | Field | DocType |
Polynomial Ring,Formal Power Series,Hilbert Series,Noetherian Ring,Hilbert Function | Topology,Discrete mathematics,Combinatorics,Noetherian ring,Polynomial,Polynomial ring,Commutative algebra,Hilbert series and Hilbert polynomial,Formal power series,Gröbner basis,Hilbert–Poincaré series,Mathematics | Journal |
Volume | Issue | ISSN |
6 | 2 | 0179-5376 |
Citations | PageRank | References |
13 | 3.06 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Louis J. Billera | 1 | 279 | 57.41 |
| Lauren L. Rose | 2 | 16 | 3.72 |