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The Hamiltonian cycle in the Cayley graph of the symmetric group generated by the Steinhaus–Johnson–Trotter algorithm Wheel diagram of all permutations of length = generated by the Steinhaus-Johnson-Trotter algorithm, where each permutation is color-coded (1=blue, 2=green, 3=yellow, 4=red).
Let be a metric space with distance function .Let be a set of indices and let () be a tuple (indexed collection) of nonempty subsets (the sites) in the space .The Voronoi cell, or Voronoi region, , associated with the site is the set of all points in whose distance to is not greater than their distance to the other sites , where is any index different from .
The graph of the constant function y = c is a horizontal line in the plane that passes through the point (0, c). [2] In the context of a polynomial in one variable x, the constant function is called non-zero constant function because it is a polynomial of degree 0, and its general form is f(x) = c, where c is nonzero.
A cone with vertex N of a diagram D : J → C is a morphism from the constant diagram Δ(N) to D. The constant diagram is the diagram which sends every object of J to an object N of C and every morphism to the identity morphism on N. The limit of a diagram D is a universal cone to D. That is, a cone through which all other cones uniquely factor.
[1] [2] The terms mathematical constant or physical constant are sometimes used to distinguish this meaning. [3] A function whose value remains unchanged (i.e., a constant function). [4] Such a constant is commonly represented by a variable which does not depend on the main variable(s) in question.
The [5 dl 2 dl 1 dl 2 dl] represents a dash-dot line. There are 5 units of line (the dash) followed by 2 units of empty space, 1 unit of line (the dot), 2 more units of empty space, and then it starts over again. 0.5 0.5 0.5 represents the color gray. /LTb is the graph's border, and /LTa is for the zero axes. [9]
In general, a Grassmann algebra on n generators can be represented by 2 n × 2 n square matrices. Physically, these matrices can be thought of as raising operators acting on a Hilbert space of n identical fermions in the occupation number basis. Since the occupation number for each fermion is 0 or 1, there are 2 n possible basis states ...
The Cheeger constant as a measure of "bottleneckedness" is of great interest in many areas: for example, constructing well-connected networks of computers, card shuffling. The graph theoretical notion originated after the Cheeger isoperimetric constant of a compact Riemannian manifold. The Cheeger constant is named after the mathematician Jeff ...