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An integer whose decimal digits contain no zeros is said to be zerofree. The first few positive zerofree integers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, ...

van der Waerden's theorem is a theorem about the existence of arithmetic progressions in sets. The theorem can be stated in four equivalent forms. 1. If N=C_1 union C_2 union ...

The Gewirtz graph, sometimes also called the Sims-Gewirtz graph (Brouwer), is an integral graph on 56 nodes and 280 edges that is also a regular graph of order 10. It is ...

A polygon can be defined (as illustrated above) as a geometric object "consisting of a number of points (called vertices) and an equal number of line segments (called sides), ...

The Sierpiński sieve is a fractal described by Sierpiński in 1915 and appearing in Italian art from the 13th century (Wolfram 2002, p. 43). It is also called the Sierpiński ...

A simple graph, also called a strict graph (Tutte 1998, p. 2), is an unweighted, undirected graph containing no graph loops or multiple edges (Gibbons 1985, p. 2; West 2000, ...

Perfect numbers are positive integers n such that n=s(n), (1) where s(n) is the restricted divisor function (i.e., the sum of proper divisors of n), or equivalently ...

The Alexander polynomial is a knot invariant discovered in 1923 by J. W. Alexander (Alexander 1928). The Alexander polynomial remained the only known knot polynomial until ...

The chromatic number of a graph G is the smallest number of colors needed to color the vertices of G so that no two adjacent vertices share the same color (Skiena 1990, p. ...

A complete tripartite graph is the k=3 case of a complete k-partite graph. In other words, it is a tripartite graph (i.e., a set of graph vertices decomposed into three ...