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Given n matches (i.e., rigid unit line segments), find the number of topologically distinct planar arrangements which can be made (Gardner 1991). In this problem, two matches ...

A maximal independent edge set of a graph is an independent edge set that cannot be expanded to another independent edge set by addition of any edge in the graph. Note that a ...

A maximal irredundant set is an irredundant set that cannot be expanded to another irredundant set by addition of any vertex in the graph. Note that a maximal irredundant set ...

The index associated to a metric tensor g on a smooth manifold M is a nonnegative integer I for which index(gx)=I for all x in M. Here, the notation index(gx) denotes the ...

A fractal curve created from the base curve and motif illustrated above (Lauwerier 1991, p. 37). As illustrated above, the number of segments after the nth iteration is ...

A monotonic matrix of order n is an n×n matrix in which every element is either 0 or contains a number from the set {1,...,n} subject to the conditions 1. The filled-in ...

In a monoid or multiplicative group where the operation is a product ·, the multiplicative inverse of any element g is the element g^(-1) such that g·g^(-1)=g^(-1)·g=1, with ...

Let A, B, and C be three circles in the plane, and let X be any circle touching B and C. Then build up a chain of circles such that Y:CAX, Z:ABY, X^':BCZ, Y^':CAX^', ...

The following table gives the number of nonadjacent vertex pairs k on graphs of n=1, 2, ... vertices. k counts 1 0, 1, 1, 1, 1, 1, 1, ... 2 0, 0, 1, 2, 2, 2, 2, ... 3 0, 0, ...

There are a number of attractive polyhedron compounds consisting of two octahedra. The first (left figure) consists of two octahedra rotated above a common C_3 symmetry axes. ...