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4,067
Quantum complexity of testing group commutativity
 Proceedings of ICALP’05
, 2005
"... Abstract. We consider the problem of testing the commutativity of a blackbox group specified by its k generators. The complexity (in terms of k) of this problem was first considered by Pak, who gave a randomized algorithm involving O(k) group operations. We construct a quite optimal quantum algorit ..."
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Cited by 30 (5 self)
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Abstract. We consider the problem of testing the commutativity of a blackbox group specified by its k generators. The complexity (in terms of k) of this problem was first considered by Pak, who gave a randomized algorithm involving O(k) group operations. We construct a quite optimal quantum
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 n2 lower bound for the number of pairs (a, b) of elements with ab ̸ = ba 3 in ..."
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in every noncommutative group of size n. It implies a constant time randomized algorithm that tests if a group of n elements is commutative. Our lower bound for the number of noncommutative pairs (a, b) (ab ̸ = ba) in a noncommutative group of size n has a generalized format (p−1)(q−1)n2, pq where p
Algebraic Graph Theory
, 2011
"... Algebraic graph theory comprises both the study of algebraic objects arising in connection with graphs, for example, automorphism groups of graphs along with the use of algebraic tools to establish interesting properties of combinatorial objects. One of the oldest themes in the area is the investiga ..."
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Cited by 892 (13 self)
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Algebraic graph theory comprises both the study of algebraic objects arising in connection with graphs, for example, automorphism groups of graphs along with the use of algebraic tools to establish interesting properties of combinatorial objects. One of the oldest themes in the area
PERMUTATION REPRESENTATIONS OF THE BRAID GROUP COMMUTATOR SUBGROUP.
, 2005
"... Abstract. We study the representations of the commutator subgroup Kn of the braid group Bn into the symmetric group Sr. Motivated by some experimental results, we conjecture that every such a representation with n> r must be trivial. 1. ..."
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Cited by 1 (0 self)
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Abstract. We study the representations of the commutator subgroup Kn of the braid group Bn into the symmetric group Sr. Motivated by some experimental results, we conjecture that every such a representation with n> r must be trivial. 1.
FINITE REPRESENTATIONS OF THE BRAID GROUP COMMUTATOR SUBGROUP
, 704
"... Abstract. We study the representations of the commutator subgroup Kn of the braid group Bn into a finite group Σ. This is done through a symbolic dynamical system. Some experimental results enable us to compute the number of subgroups of Kn of a given (finite) index, and, as a byproduct, to recover ..."
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Abstract. We study the representations of the commutator subgroup Kn of the braid group Bn into a finite group Σ. This is done through a symbolic dynamical system. Some experimental results enable us to compute the number of subgroups of Kn of a given (finite) index, and, as a by
Gravity coupled with matter and the foundation of non commutative geometry
, 1996
"... We first exhibit in the commutative case the simple algebraic relations between the algebra of functions on a manifold and its infinitesimal length element ds. Its unitary representations correspond to Riemannian metrics and Spin structure while ds is the Dirac propagator ds = ×— × = D −1 where D i ..."
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Cited by 343 (17 self)
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work with Ali Chamseddine) to give the SM Lagrangian coupled to gravity. The internal fluctuations of the non commutative geometry are trivial in the commutative case but yield the full bosonic sector of SM with all correct quantum numbers in the slightly non commutative case. The group of local gauge
Convexity and commuting Hamiltonians
 Bull. London Math. Soc.,14
, 1982
"... A wellknown result of Schur [9] asserts that the diagonal elements (al,..., an) of annxn Hermitian matrix A satisfy a system of linear inequalities involving the eigenvalues (Xi,..., Xn). In geometric terms, regarding a and k as points in R " and allowing the symmetric group £ „ to act by perm ..."
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Cited by 220 (1 self)
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A wellknown result of Schur [9] asserts that the diagonal elements (al,..., an) of annxn Hermitian matrix A satisfy a system of linear inequalities involving the eigenvalues (Xi,..., Xn). In geometric terms, regarding a and k as points in R " and allowing the symmetric group £ „ to act
Commuter
"... Erie International Airport (elevation 733 feet above mean sea level) is a primary commercial service facility which accommodates aircraft from Airplane Design Groups I, II, and III, and Aircraft Approach Categories A, B and C. The Airport currently has an Airport Reference Code (ARC) of CIII. Thus, ..."
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daily departures, or 22 % of total departures. Commuter operations accounted for 14 departures or 78 % of the total departures. The characteristics of the aircraft utilized and how they relate to the FAA’s classifications of design group and approach categories are presented in Table D1.
ITERATION GROUPS, COMMUTING FUNCTIONS AND SIMULTANEOUS SYSTEMS OF LINEAR FUNCTIONAL EQUATIONS Abstract. Let
"... f t t∈R be a measurable iteration group on an open interval I. Under some conditions, we prove that the inequalies g ◦ fa ≤ fa ◦ g and g ◦ fb ≤ fb ◦ g for some a, b ∈ R imply that g must belong to the iteration group. Some weak conditions under which two iteration groups have to consist of the same ..."
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elements are given. An extension theorem of a local solution of a simultaneous system of iterative linear functional equations is presented and applied to prove that, under some conditions, if a function g commutes in a neighbourhood of f with two suitably chosen elements fa and fb of an iteration group
Results 1  10
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4,067