共查询到20条相似文献,搜索用时 15 毫秒
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The linear discrepancy of a poset P is the least k such that there is a linear extension L of P such that if x and y are incomparable, then |hL(x)−hL(y)|≤k, whereas the weak discrepancy is the least k such that there is a weak extension W of P such that if x and y are incomparable, then |hW(x)−hW(y)|≤k. This paper resolves a question of Tanenbaum, Trenk, and Fishburn on characterizing when the weak and linear discrepancy of a poset are equal. Although it is shown that determining whether a poset has equal weak and linear discrepancy is -complete, this paper provides a complete characterization of the minimal posets with equal weak and linear discrepancy. Further, these minimal posets can be completely described as a family of interval orders. 相似文献
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Róbert Szőke 《Acta Mathematica Hungarica》2006,111(1-2):77-79
Summary We show that an isometry between not locally hyperk?hler, locally irreducible K?hler manifolds is either holomorphic or antiholomorphic. 相似文献
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We show that for arbitrary fixed conjugacy classes C1,…,Cl, l?3, of loxodromic isometries of the two-dimensional complex or quaternionic hyperbolic space there exist isometries g1,…,gl, where each gi∈Ci, and whose product is the identity. The result follows from the properness, up to conjugation, of the multiplication map on a pair of conjugacy classes in rank 1 groups. 相似文献
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A.M. Vershik 《Topology and its Applications》2008,155(14):1618-1626
We prove the equivalence of the two important facts about finite metric spaces and universal Urysohn metric spaces U, namely Theorems A and G: Theorem A (Approximation): The group of isometry ISO(U) contains everywhere dense locally finite subgroup; Theorem G (Globalization): For each finite metric space F there exists another finite metric space and isometric imbedding j of F to such that isometry j induces the imbedding of the group monomorphism of the group of isometries of the space F to the group of isometries of space and each partial isometry of F can be extended up to global isometry in . The fact that Theorem G, is true was announced in 2005 by author without proof, and was proved by S. Solecki in [S. Solecki, Extending partial isometries, Israel J. Math. 150 (2005) 315-332] (see also [V. Pestov, The isometry group of the Urysohn space as a Lévy group, Topology Appl. 154 (10) (2007) 2173-2184; V. Pestov, A theorem of Hrushevski-Solecki-Vershik applied to uniform and coarse embeddings of the Urysohn metric space, math/0702207]) based on the previous complicate results of other authors. The theorem is generalization of the Hrushevski's theorem about the globalization of the partial isomorphisms of finite graphs. We intend to give a constructive proof in the same spirit for metric spaces elsewhere. We also give the strengthening of homogeneity of Urysohn space and in the last paragraph we gave a short survey of the various constructions of Urysohn space including the new proof of the construction of shift invariant universal distance matrix from [P. Cameron, A. Vershik, Some isometry groups of Urysohn spaces, Ann. Pure Appl. Logic 143 (1-3) (2006) 70-78]. 相似文献
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We prove that the poset algebra of every scattered poset with finite width is embeddable in the poset algebra of a well ordered poset.Mathematics Subject Classification (2000):Primary 03G05, 06A06, 06A11; Secondary 08A05, 54G12 相似文献
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We derive the Singleton bound for poset codes and define the MDS poset codes as linear codes which attain the Singleton bound.
In this paper, we study the basic properties of MDS poset codes. First, we introduce the concept of I-perfect codes and describe the MDS poset codes in terms of I-perfect codes. Next, we study the weight distribution of an MDS poset code and show that the weight distribution of an MDS
poset code is completely determined. Finally, we prove the duality theorem which states that a linear code C is an MDS -code if and only if is an MDS -code, where is the dual code of C and is the dual poset of
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Reinhard C. Laubenbacher 《K-Theory》1993,7(1):17-21
LetS be a finite partially ordered set andk a field. This paper relates the algebraicK-theory ring of the category ofk-representations ofS to the Möbius ring ofS. 相似文献
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Scot Adams 《Geometriae Dedicata》2004,105(1):1-12
We give an alternate proof of N. Kowalsky's theorem describing the collection of connected simple Lie groups with finite center
which admit a nontrivial, nonproper action by isometries of a connected Lorentz manifold. 相似文献
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The linear discrepancy of a poset P is the least k such that there is a linear extension L of P such that if x and y are incomparable in P, then |h
L
(x)–h
L
(y)|≤k, where h
L
(x) is the height of x in L. Tanenbaum, Trenk, and Fishburn characterized the posets of linear discrepancy 1 as the semiorders of width 2 and posed the
problem of characterizing the posets of linear discrepancy 2. We show that this problem is equivalent to finding the posets
with linear discrepancy equal to 3 having the property that the deletion of any point results in a reduction in the linear
discrepancy. Howard determined that there are infinitely many such posets of width 2. We complete the forbidden subposet characterization
of posets with linear discrepancy equal to 2 by finding the minimal posets of width 3 with linear discrepancy equal to 3.
We do so by showing that, with a small number of exceptions, they can all be derived from the list for width 2 by the removal
of specific comparisons.
The first and second authors were supported during this research by National Science Foundation VIGRE grant DMS-0135290. 相似文献
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Esteban Andruchow 《Journal of Mathematical Analysis and Applications》2008,337(2):1226-1237
We study the geometry of the set
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Kelly Kross Jordan 《Journal of Combinatorial Theory, Series A》2010,117(6):625-641
Let Nn denote the quotient poset of the Boolean lattice, Bn, under the relation equivalence under rotation. Griggs, Killian, and Savage proved that Np is a symmetric chain order for prime p. In this paper, we settle the question posed in that paper, namely whether Nn is a symmetric chain order for all n. This paper provides an algorithm that produces a symmetric chain decomposition (or SCD). We accomplish this by modifying bracketing from Greene and Kleitman. This allows us to take appropriate “middles” of certain chains from the Greene-Kleitman SCD for Bn. We also prove additional properties of the resulting SCD and show that this settles a related conjecture. 相似文献
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The generalized Hamming weights of a linear code have been extensively studied since Wei first use them to characterize the cryptography performance of a linear code over the wire-tap channel of type II. In this paper, we investigate the generalized Hamming weights of three classes of linear codes constructed through defining sets and determine them partly for some cases. Particularly, in the semiprimitive case we solve a problem left in Yang et al. (2015) [30]. 相似文献
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In this paper, a class of -ary linear codes with two weights is constructed by using the properties of cyclotomic classes of . The complete weight enumerators of these linear codes are also determined. In some cases, they are optimal and can be employed to obtain secret sharing schemes with interesting access structures and asymptotically optimal systematic authentication codes. 相似文献
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研究了量子纠错码的等价性和保距同构,推广了Bogart等人的一些概念,并给出若干基本定理,这些定理对进一步研究量子码的等价性和保距同构是非常有用的.在此基础上构造出一个反例,证明了在量子情形下,MacWmiams的一个重要定理不成立. 相似文献