Polynomial Invariants and Harmonic Functions Related to Exceptional Regular Polytopes
نویسندگان
چکیده
regular polytopes, mean value property, finite reflection groups We compute certain polynomial invariants for the finite reflection groups of the types H3, H4 and F4. Using this result, we explicitly determine the solution space of functions satisfying a mean value property related to the exceptional regular polytopes, namely, the icosahedron and dodecahedron in three dimensions and the 24-cell, 600-cell, and 120-cell in four dimensions.
منابع مشابه
Rigidity and Polynomial Invariants of Convex Polytopes
We present an algebraic approach to the classical problem of constructing a simplicial convex polytope given its planar triangulation and lengths of its edges. We introduce polynomial invariants of a polytope and show that they satisfy polynomial relations in terms of squares of edge lengths. We obtain sharp upper and lower bounds on the degree of these polynomial relations. In a special case o...
متن کاملValuative invariants for polymatroids
Many important invariants for matroids and polymatroids, such as the Tutte polynomial, the Billera-JiaReiner quasi-symmetric function, and the invariant G introduced by the first author, are valuative. In this paper we construct the Z-modules of all Z-valued valuative functions for labeled matroids and polymatroids on a fixed ground set, and their unlabeled counterparts, the Z-modules of valuat...
متن کاملInvariants for Polymatroids
Many important invariants for matroids and polymatroids, such as the Tutte polynomial, the Billera-Jia-Reiner quasi-symmetric function, and the invariant G introduced by the first author, are valuative. In this paper we construct the Z-modules of all Z-valued valuative functions for labeled matroids and polymatroids on a fixed ground set, and their unlabeled counterparts, the Z-modules of valua...
متن کاملExact Euler Maclaurin Formulas for Simple Lattice Polytopes
Euler Maclaurin formulas for a polytope express the sum of the values of a function over the lattice points in the polytope in terms of integrals of the function and its derivatives over faces of the polytope or its dilations. There are two kinds of Euler Maclaurin formulas: exact formulas, which apply to exponential or polynomial functions, and formulas with remainder, which apply to arbitrary...
متن کاملEinladung Im Oberseminar Reelle Geometrie Und Algebra Hält Coercive Polynomials and Their Newton Polytopes
Many interesting properties of polynomials are closely related to the geometry of their Newton polytopes. We analyze the coercivity on R of multivariate polynomials f ∈ R[x] in terms of their Newton polytopes. In fact, we introduce the broad class of so-called gem regular polynomials and characterize their coercivity via conditions imposed on the vertex set of their Newton polytopes. These cond...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Experimental Mathematics
دوره 11 شماره
صفحات -
تاریخ انتشار 2002