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The odd graph O_n of order n is a graph having vertices given by the (n-1)-subsets of {1,...,2n-1} such that two vertices are connected by an edge iff the associated subsets ...

Let N steps of equal length be taken along a line. Let p be the probability of taking a step to the right, q the probability of taking a step to the left, n_1 the number of ...

The utility problem posits three houses and three utility companies--say, gas, electric, and water--and asks if each utility can be connected to each house without having any ...

The word polytope is used to mean a number of related, but slightly different mathematical objects. A convex polytope may be defined as the convex hull of a finite set of ...

For a single variate X having a distribution P(x) with known population mean mu, the population variance var(X), commonly also written sigma^2, is defined as ...

The adjacency list representation of a graph consists of n lists one for each vertex v_i, 1<=i<=n, which gives the vertices to which v_i is adjacent. The adjacency lists of a ...

An algebraic manifold is another name for a smooth algebraic variety. It can be covered by coordinate charts so that the transition functions are given by rational functions. ...

Let M^n be a compact n-dimensional oriented Riemannian manifold without boundary, let O be a group representation of pi_1(M) by orthogonal matrices, and let E(O) be the ...

Define an antipode of a given graph vertex v_i as a vertex v_j at greatest possible graph distance from v_i. Then an antipodal graph is a connected graph in which each vertex ...

The best known example of an Anosov diffeomorphism. It is given by the transformation [x_(n+1); y_(n+1)]=[1 1; 1 2][x_n; y_n], (1) where x_(n+1) and y_(n+1) are computed mod ...