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961.
We investigate the computational complexity of finding an element of a permutation group H⊆Sn with minimal distance to a given π∈Sn, for different metrics on Sn. We assume that H is given by a set of generators. In particular, the size of H might be exponential in the input size, so that in general the problem cannot be solved in polynomial time by exhaustive enumeration. For the case of the Cayley Distance, this problem has been shown to be NP-hard, even if H is abelian of exponent two [R.G.E. Pinch, The distance of a permutation from a subgroup of Sn, in: G. Brightwell, I. Leader, A. Scott, A. Thomason (Eds.), Combinatorics and Probability, Cambridge University Press, 2007, pp. 473-479]. We present a much simpler proof for this result, which also works for the Hamming Distance, the lp distance, Lee’s Distance, Kendall’s tau, and Ulam’s Distance. Moreover, we give an NP-hardness proof for the l∞ distance using a different reduction idea. Finally, we discuss the complexity of the corresponding fixed-parameter and maximization problems. 相似文献
962.
We consider linearly ordered, Archimedean dimension groups (G,G+,u) for which the group G/u is torsion-free. It will be shown that if, in addition, G/u is generated by a single element (i.e., ), then (G,G+,u) is isomorphic to for some irrational number τ(0,1). This amounts to an extension of related results where dimension groups for which G/u is torsion were considered. We will prove, in the case of the Fibonacci dimension group, that these results can be used to directly construct an equivalence relation groupoid whose C*-algebra is the Fibonacci C*-algebra. 相似文献
963.
Let V be a quadratic space with a form q over an arbitrary local field F of characteristic different from 2. Let with the form Q extending q with Q(e) = 1. Consider the standard embedding and the two-sided action of on . In this note we show that any -invariant distribution on is invariant with respect to transposition. This result was earlier proven in a bit different form in van Dijk (Math Z 193:581–593,
1986) for , in Aparicio and van Dijk (Complex generalized Gelfand pairs. Tambov University, 2006) for and in Bosman and van Dijk (Geometriae Dedicata 50:261–282, 1994) for p-adic fields. Here we give a different proof. Using results from Aizenbud et al. (arXiv:0709.1273 (math.RT), submitted), we
show that this result on invariant distributions implies that the pair (O(V), O(W)) is a Gelfand pair. In the archimedean setting this means that for any irreducible admissible smooth Fréchet representation
(π, E) of we have A stronger result for p-adic fields is obtained in Aizenbud et al. (arXiv:0709.4215 (math.RT), submitted). 相似文献
964.
The Hecke group algebra of a finite Coxeter group , as introduced by the first and last authors, is obtained from by gluing appropriately its 0-Hecke algebra and its group algebra. In this paper, we give an equivalent alternative construction in the case when is the finite Weyl group associated to an affine Weyl group W. Namely, we prove that, for q not a root of unity of small order, is the natural quotient of the affine Hecke algebra H(W)(q) through its level 0 representation.The proof relies on the following core combinatorial result: at level 0 the 0-Hecke algebra H(W)(0) acts transitively on . Equivalently, in type A, a word written on a circle can be both sorted and antisorted by elementary bubble sort operators. We further show that the level 0 representation is a calibrated principal series representation M(t) for a suitable choice of character t, so that the quotient factors (non-trivially) through the principal central specialization. This explains in particular the similarities between the representation theory of the 0-Hecke algebra and that of the affine Hecke algebra H(W)(q) at this specialization. 相似文献
965.
Amy M. Fu 《Journal of Combinatorial Theory, Series A》2009,116(4):903-917
We give non-symmetric versions of the Cauchy kernel and Littlewood's kernels, corresponding to the types A, B, C and D, of the classical groups. Defining two families of key polynomials (one of them being the Demazure characters), we show that these new kernels are diagonal in the basis of key polynomials. We define scalar products such that the two families of key polynomials are adjoint to each other. 相似文献
966.
Shuzhou Wang 《Journal of Functional Analysis》2009,256(10):3313-3341
The notion of simple compact quantum group is introduced. As non-trivial (noncommutative and noncocommutative) examples, the following families of compact quantum groups are shown to be simple: (a) The universal quantum groups Bu(Q) for Q∈GL(n,C) satisfying , n?2; (b) The quantum automorphism groups Aaut(B,τ) of finite-dimensional C∗-algebras B endowed with the canonical trace τ when dim(B)?4, including the quantum permutation groups Aaut(Xn) on n points (n?4); (c) The standard deformations Kq of simple compact Lie groups K and their twists , as well as Rieffel's deformation KJ. 相似文献
967.
Mattia Perrone 《Journal of Functional Analysis》2009,256(11):3471-3489
We study Haagerup inequality for radial functions on uniform lattices in semisimple Lie groups, with respect to Riemannian metrics and, in some case, to word metrics. In particular we extend the Swiatkowski-Valette results to any lattice acting properly and essentially transitively on classical buildings. 相似文献
968.
Robert C. Rhoades 《Journal of Number Theory》2009,129(6):1379-1391
We take an approach toward counting the number of integers n for which the curve En: y2=x3−n2x has 2-Selmer groups of a given size. This question was also discussed in a pair of papers by Roger Heath-Brown. In contrast to earlier work, our analysis focuses on restricting the number of prime factors of n. Additionally, we discuss the connection between computing the size of these Selmer groups and verifying cases of the Birch and Swinnerton-Dyer Conjecture. The key ingredient for the asymptotic formulae is the “independence” of the Legendre symbol evaluated at the prime divisors of an integer with exactly k prime factors. 相似文献
969.
The closed model category of exterior spaces, that contains the proper category, is a useful tool for the study of non compact
spaces and manifolds. The notion of exterior weak ℕ-S-equivalences is given by exterior maps which induce isomorphisms on the k-th ℕ-exterior homotopy groups for k ∈ S, where S is a set of non negative integers. The category of exterior spaces with a base ray localized by exterior weak ℕ-S-equivalences is called the category of exterior ℕ-S-types. The existence of closed model structures in the category of exterior spaces permits to establish equivalences between
homotopy categories obtained by dividing by exterior homotopy relations, and categories of fractions (localized categories)
given by the inversion of classes of week equivalences. The family of neighbourhoods ‘at infinity’ of an exterior space can
be interpreted as a global prospace and under the condition of first countable at infinity we can consider a global tower
instead of a prospace. The objective of this paper is to use localized categories to find the connection between S-types of exterior spaces and S-types of global towers of spaces. The main result of this paper establishes an equivalence between the category of S-types of rayed first countable exterior spaces and the category of S-types of global towers of pointed spaces. As a consequence of this result, categories of global towers of algebraic models
localized up to weak equivalences can be used to give some algebraic models of S-types.
The authors acknowledge the financial support given by the projects FOMENTA 2007/03 and MTM2007-65431. 相似文献
970.
主要探讨了秩大于或者等于p-1的可除阿贝尔p-群的p-自同构群,并且得到这些p-自同构如何作用在该可除阿贝尔p-群上.这些结论有助于进一步理解 ?ernikov p-群的结构. 相似文献