منابع مشابه
Figurative Tours and Braids
We start with a rectangular grid of points, and we connect pairs of points to form either a tour (a Hamiltonian cycle) or a braid (a collection of disjoint paths that start in the top row and end on the bottom). In each case, our goal is to design a graph that will closely resemble a grayscale target image when viewed from a distance. From up close, the graph will look like an abstract pattern....
متن کاملBraids and Permutations
E. Artin described all irreducible representations of the braid group B k to the symmetric group S(k). We strengthen some of his results and, moreover, exhibit a complete picture of homomorphisms ψ : B k → S(n) for n ≤ 2k. We show that the image Im ψ of ψ is cyclic whenever either (*) n < k = 4 or (* *) ψ is irreducible and 6 < k < n < 2k. For k > 6 there exist, up to conjugation, exactly 3 irr...
متن کاملBraids and differential equations
Forcing theorems based on topological features of invariant sets have played a fundamental role in dynamics and differential equations. This talk focuses on the recent work of Vandervorst, Van den Berg, and the author using braids to construct a forcing theory for scalar parabolic PDEs, second-order Lagrangian ODEs, and one-dimensional lattice dynamics. Mathematics Subject Classification (2000)...
متن کاملBraids and crossed modules
For n ≥ 4, we describe Artin’s braid group on n strings as a crossed module over itself. In particular, we interpret the braid relations as crossed module structure relations. Subject classification: Primary: 20F36 57M05 57M20 57M25; Secondary: 18D50 18G55 20C08 55P48
متن کاملBraids, Posets and Orthoschemes
In this article we study the curvature properties of the order complex of a graded poset under a metric that we call the “orthoscheme metric”. In addition to other results, we characterize which rank 4 posets have CAT(0) orthoscheme complexes and by applying this theorem to standard posets and complexes associated with four-generator Artin groups, we are able to show that the 5-string braid gro...
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ژورنال
عنوان ژورنال: Physical Review A
سال: 1991
ISSN: 1050-2947,1094-1622
DOI: 10.1103/physreva.44.r3419