Results 31 to 40 of about 2,228 (168)

Presentations of graph braid groups [PDF]

Forum Mathematicum, 2012
Abstract. Let be a graph. The (unlabeled) configuration space of n points on is the space of n-element subsets of . The n-strand braid group of , denoted , is the fundamental group of . This paper applies the methods of discrete Morse theory to the spaces .
Farley, Daniel, Sabalka, Lucas
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Open-string integrals with multiple unintegrated punctures at genus one

Journal of High Energy Physics, 2022
We study integrals appearing in intermediate steps of one-loop open-string amplitudes, with multiple unintegrated punctures on the A-cycle of a torus. We construct a vector of such integrals which closes after taking a total differential with respect to ...
André Kaderli, Carlos Rodriguez
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Braid Groups are Linear Groups

Advances in Mathematics, 1996
Let \(B_n\) denote the braid group on \(n\) strings. \(B_2\) is infinite cyclic and hence is a linear group. It is well-known that \(B_3\) is also a linear group. But it has remained an open problem as to whether any other braid groups are linear.
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Random subgroups and analysis of the length-based and quotient attacks

Journal of Mathematical Cryptology, 2008
In this paper we discuss generic properties of “random subgroups” of a given group G. It turns out that in many groups G (even in most exotic of them) the random subgroups have a simple algebraic structure and they “sit” inside G in a very particular way.
Myasnikov Alexei G., Ushakov Alexander
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BRAID GROUP CRYPTOGRAPHY

, 2009
In the last decade, a number of public key cryptosystems based on com- binatorial group theoretic problems in braid groups have been proposed. We survey these cryptosystems and some known attacks on them. This survey includes: Basic facts on braid groups and on the Garside normal form of its elements, some known algorithms for solving the word problem ...
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Braided groups

Journal of Pure and Applied Algebra, 1993
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A BRAIDED SIMPLICIAL GROUP [PDF]

Proceedings of the London Mathematical Society, 2002
By studying the braid group action on Milnor's construction of the 1-sphere, we show that the general higher homotopy group of the 3-sphere is the fixed set of the pure braid group action on certain combinatorially described groups. This establishes a relation between the braid groups and the homotopy groups of the sphere.2000Mathematical Subject ...
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Z₂ Topological Order and Topological Protection of Majorana Fermion Qubits

Condensed Matter, 2021
The Kitaev chain model exhibits topological order that manifests as topological degeneracy, Majorana edge modes and Z2 topological invariant of the bulk spectrum.
Rukhsan Ul Haq, Louis H. Kauffman
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Mean-set attack: cryptanalysis of Sibert et al. authentication protocol

Journal of Mathematical Cryptology, 2010
We analyze the Sibert et al. group-based (Feige–Fiat–Shamir type) authentication protocol and show that the protocol is not computationally zero-knowledge.
Mosina Natalia, Ushakov Alexander
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Double Affine Hecke Algebras of Rank 1 and the Z_3-Symmetric Askey-Wilson Relations

Symmetry, Integrability and Geometry: Methods and Applications, 2010
We consider the double affine Hecke algebra H=H(k_0,k_1,k_0^v,k_1^v;q) associated with the root system (C_1^v,C_1). We display three elements x, y, z in H that satisfy essentially the Z_3-symmetric Askey-Wilson relations.
Paul Terwilliger, Tatsuro Ito
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