منابع مشابه
Testing Group Commutativity in Constant Time
Lipton and Zalcstein presented a constant time algorithm for testing if a group is abelian in 12. However, the reference only contains a short abstract without proof. In this paper, we give a self contained proof for an n 2 3 lower bound for the number of pairs (a, b) of elements with ab 6= ba in every non-commutative group of size n. It implies a constant time randomized algorithm that tests i...
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Let R be a set of red points and B a set of blue points on the plane. In this paper we introduce a new concept for measuring how mixed the elements of S = R ∪ B are. The discrepancy of a set X ⊆ S is ||X ∩ R| − |X ∩ B||. We say that a partition Π = {S1, S2, . . . , Sk} of S is convex if the convex hulls of its members are pairwise disjoint. The discrepancy of a convex partition of S is the mini...
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Let G be a group generated by k elements G = ⟨g1, . . . , gk⟩, with group operations (multiplication, inversion, comparison with id) performed by a black box. We prove that one can test whether the group G is abelian at a cost of O(k) group operations. On the other hand, we show that deterministic approach requires Ω(k) group operations.
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Abstract. The poset of noncrossing partitions can be naturally defined for any finite Coxeter group W . It is a self-dual, graded lattice which reduces to the classical lattice of noncrossing partitions of {1, 2, . . . , n} defined by Kreweras in 1972 when W is the symmetric group Sn, and to its type B analogue defined by the second author in 1997 when W is the hyperoctahedral group. We give a ...
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ژورنال
عنوان ژورنال: International Electronic Journal of Algebra
سال: 2019
ISSN: 1306-6048
DOI: 10.24330/ieja.504159