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91.
A Coxeter matroid is a generalization of matroid, ordinary matroid being the case corresponding to the family of Coxeter groups A
n
, which are isomorphic to the symmetric groups. A basic result in the subject is a geometric characterization of Coxeter matroid in terms of the matroid polytope, a result first stated by Gelfand and Serganova. This paper concerns properties of the matroid polytope. In particular, a criterion is given for adjacency of vertices in the matroid polytope. 相似文献
92.
非自伴非紧的抽象边值问题 总被引:4,自引:0,他引:4
在Hilbert空间研究了一类非自伴非紧的抽象边值问题,利用Wiener-Hopf方法构造了空间X的分裂投影,进而得出了方程解的适定性. 相似文献
93.
Increasing convex-along-rays functions are defined within an abstract convexity framework. The basic properties of these functions including support sets and subdifferentials are outlined. Applications are provided to unconstrained global optimization using the concept of excess function. 相似文献
94.
In this paper we lay the foundations for the study of permutation polytopes: the convex hull of a group of permutation matrices.We clarify the relevant notions of equivalence, prove a product theorem, and discuss centrally symmetric permutation polytopes. We provide a number of combinatorial properties of (faces of) permutation polytopes. As an application, we classify ?4-dimensional permutation polytopes and the corresponding permutation groups. Classification results and further examples are made available online.We conclude with several questions suggested by a general finiteness result. 相似文献
95.
There are only finitely many locally projective regular polytopes of type {5, 3, 5}. They are covered by a locally spherical polytope whose automorphism group is J1×J1×L2(19), where J1 is the first Janko group, of order 175560, and L2(19) is the projective special linear group of order 3420. This polytope is minimal, in the sense that any other polytope that covers all locally projective polytopes of type {5, 3, 5} must in turn cover this one. 相似文献
96.
97.
We consider compact hyperbolic Coxeter polytopes whose Coxeter diagram contains a unique dotted edge. We prove that such a polytope in d-dimensional hyperbolic space has at most d+3 facets. In view of results by Kaplinskaja [I.M. Kaplinskaya, Discrete groups generated by reflections in the faces of simplicial prisms in Lobachevskian spaces, Math. Notes 15 (1974) 88-91] and the second author [P. Tumarkin, Compact hyperbolic Coxeter n-polytopes with n+3 facets, Electron. J. Combin. 14 (2007), R69, 36 pp.], this implies that compact hyperbolic Coxeter polytopes with a unique pair of non-intersecting facets are completely classified. They do exist only up to dimension 6 and in dimension 8. 相似文献
98.
We present a multivariate generating function for all n×n nonnegative integral matrices with all row and column sums equal to a positive integer t, the so called semi-magic squares. As a consequence we obtain formulas for all coefficients of the Ehrhart polynomial of
the polytope B
n
of n×n doubly-stochastic matrices, also known as the Birkhoff polytope. In particular we derive formulas for the volumes of B
n
and any of its faces. 相似文献
99.
讨论抽象基(特别是偏序集带辅助序)上的伪Scott拓扑与伪Scott开滤子集的一些基本性质, 推广了Domain理论中一些熟知的结论,证明了抽象基上的伪Scott拓扑是完全分配格;若在偏序集P上赋予辅助关系<, 则其上伪Scott开滤子之集是连续domain. 相似文献
100.