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A curve created by starting with a circle, dividing it into six arcs, and flipping three alternating arcs. The process is then repeated an infinite number of times.

A group having an infinite number of elements. Some infinite groups, such as the integers or rationals, are not continuous groups.

The sequence generated by repeated application of a map. The map is said to have a closed orbit if it has a finite number of elements.

A vertex coloring is an assignment of labels or colors to each vertex of a graph such that no edge connects two identically colored vertices. A vertex coloring that minimize ...

Topological lower bounds in terms of Betti numbers for the number of critical points form a smooth function on a smooth manifold.

The number theta in the quadric (x^2)/(a^2+theta)+(y^2)/(b^2+theta)+(z^2)/(c^2+theta)=1 is called the parameter.

A function representable as a generalized Fourier series. Let R be a metric space with metric rho(x,y). Following Bohr (1947), a continuous function x(t) for (-infty<t<infty) ...

Consider an infinite repository containing balls of n different types. Then the following table summarizes the number of distinct ways in which k balls can be picked for four ...

A bicolorable graph G is a graph with chromatic number chi(G)<=2. A graph is bicolorable iff it has no odd graph cycles (König 1950, p. 170; Skiena 1990, p. 213; Harary 1994, ...

A binary bracketing is a bracketing built up entirely of binary operations. The number of binary bracketings of n letters (Catalan's problem) are given by the Catalan numbers ...