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V. A. Kolmykov 《Mathematical Notes》2006,79(5-6):643-648
The Coxeter transformations associated with deltoids (i.e., with graphs in which all simple cycles have length 3) are considered. The structure of the set of all connected deltoids whose spectra do not contain ?1 is described. 相似文献
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V. A. Kolmykov 《Mathematical Notes》2006,79(3-4):436-439
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John R. Stembridge 《Journal of Algebraic Combinatorics》2001,13(3):275-293
We study the reduced expressions for reflections in Coxeter groups, with particular emphasis on finite Weyl groups. For example, the number of reduced expressions for any reflection can be expressed as the sum of the squares of the number of reduced expressions for certain elements naturally associated to the reflection. In the case of the longest reflection in a Weyl group, we use a theorem of Dale Peterson to provide an explicit formula for the number of reduced expressions. We also show that the reduced expressions for any Weyl group reflection are in bijection with the linear extensions of a natural partial ordering of a subset of the positive roots or co-roots. 相似文献
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Tzu-Chun Lin 《Proceedings of the American Mathematical Society》2006,134(6):1599-1604
Let be a faithful representation of a finite group over the field . Via the group acts on and hence on the algebra of homogenous polynomial functions on the vector space . R. Kane (1994) formulated the following result based on the work of R. Steinberg (1964): If the field has characteristic 0, then is a Poincaré duality algebra if and only if is a pseudoreflection group. The purpose of this note is to extend this result to the case (i.e. the order of is relatively prime to the characteristic of ).
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Mathematical Notes - 相似文献
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FU Zhi-guo 《东北数学》2006,(4)
Let ω be the element of maximal length in a finite irreducible Coxetersystem(W,S).In the present paper,we get the length of ω when(W,S)is of typeA_n B_n/C_n or D_n. 相似文献
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Christopher J. Bishop Yuval Peres 《Transactions of the American Mathematical Society》1996,348(11):4433-4445
We show that for any analytic set in , its packing dimension can be represented as , where the supremum is over all compact sets in , and denotes Hausdorff dimension. (The lower bound on packing dimension was proved by Tricot in 1982.) Moreover, the supremum above is attained, at least if . In contrast, we show that the dual quantity , is at least the ``lower packing dimension' of , but can be strictly greater. (The lower packing dimension is greater than or equal to the Hausdorff dimension.)
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It is natural to define a Coxeter transformation in quantum groups by the product of Lusztig's symmetries in some order. In this note, we show that the Ringel–Hall algebra approach enables us to determine the behavior of its action in case of finite type. 相似文献
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Xiaoyu Hu 《Stochastic Processes and their Applications》1999,80(2):249-269
Let {X(t), 0t1} be a stochastic process whose range is a random Cantor-like set depending on an -sequence (0<<1) and μ is the occupation measure of X(t). In this paper we examine the multifractal structure of μ and obtain the fractal dimensions of the sets of points of where the local dimension of μ is different from . It is interesting to notice that the final results of this paper are identical to those for the occupation measure of a stable subordinator with index , yet the stochastic process under consideration in this work is not even a Markov process. 相似文献
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By obtaining a new sufficient condition for a valid multifractal formalism, we improve in this paper a result developed by L. Olsen (1995, Adv. Math.116, 82-196). In particular, we describe a large class of measures satisfying the multifractal formalism and for which the construction of Gibbs measures is not possible. Some of these measures are not unidimensional but have a nontrivial multifractal spectrum, giving a negative answer to a question asked by S. J. Taylor (1995, J. Fourier Anal. Appl., special issue). We also describe a necessary condition of validity for the formalism which is very close to the sufficient one. This necessary condition allows us to describe a measure μ for which the multifractal packing dimension function Bμ(q) is a nontrivial real analytic function but the multifractal formalism is nowhere satisfied. This example gives also a solution to a problem posed by Taylor (cited above). 相似文献
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Reflection groups of Coxeter polyhedra in three-dimensional Thurston geometries are examined. For a wide class of Coxeter
groups, the existence of subgroups of finite index that uniformize hyperelliptic 3-manifolds is established.
Translated fromMatematicheskie Zametki, Vol. 66, No. 2, pp. 173–177, August, 1999. 相似文献
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We obtain a number of results regarding the freeness of subgroupsof Coxeter groups, Artin groups and one-relator groups withtorsion. In the case of Coxeter groups, we also obtain resultson quasiconvexity and subgroup separability. 2000 MathematicsSubject Classification 20F65, 20F55, 20F36, 20F06. 相似文献
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In this paper, we estimate the free entropy dimension of the group yon Neumann algebra(L)(Zt), which is less than 1/t,2 ≤ t ≤ ∞. This data is identical with the free dimension defined by Dykema. 相似文献
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In this paper, we estimate the free entropy dimension of the group yon Neumann algebra L(Zt), which is less than 1/t,2 ≤t ≤ +∞. This data is identical with the free dimension defined by Dykema. 相似文献
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G. C. Bell A. N. Dranishnikov 《Transactions of the American Mathematical Society》2006,358(11):4749-4764
We prove an asymptotic analog of the classical Hurewicz theorem on mappings that lower dimension. This theorem allows us to find sharp upper bound estimates for the asymptotic dimension of groups acting on finite-dimensional metric spaces and allows us to prove a useful extension theorem for asymptotic dimension. As applications we find upper bound estimates for the asymptotic dimension of nilpotent and polycyclic groups in terms of their Hirsch length. We are also able to improve the known upper bounds on the asymptotic dimension of fundamental groups of complexes of groups, amalgamated free products and the hyperbolization of metric spaces possessing the Higson property.