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Let there be n ways for a "good" selection and m ways for a "bad" selection out of a total of n+m possibilities. Take N samples and let x_i equal 1 if selection i is ...

The Meredith graph is a quartic nonhamiltonian graph on 70 nodes and 140 edges that is a counterexample to the conjecture that every 4-regular 4-connected graph is ...

Zero is the integer denoted 0 that, when used as a counting number, means that no objects are present. It is the only integer (and, in fact, the only real number) that is ...

Szemerédi's theorem states that every sequence of integers that has positive upper Banach density contains arbitrarily long arithmetic progressions. A corollary states that, ...

An isolated point of a graph is a node of degree 0 (Hartsfield and Ringel 1990, p. 8; Harary 1994, p. 15; D'Angelo and West 2000, p. 212; West 2000, p. 22). The number of ...

Every position of every impartial game has a nim-value, making it equivalent to a nim-heap. To find the nim-value (also called the Sprague-Grundy number), take the mex of the ...

For every positive integer n, there exists a circle in the plane having exactly n lattice points on its circumference. The theorem is based on the number r(n) of integral ...

A cubic symmetric graph is a symmetric cubic (i.e., regular of order 3). Such graphs were first studied by Foster (1932). They have since been the subject of much interest ...

A number x such that for all epsilon>0, there exists a member of the set y different from x such that |y-x|<epsilon. The topological definition of limit point P of A is that ...

A curvilinear polygon built up of circular arcs. The Reuleaux polygon is a generalization of the Reuleaux triangle and, for an odd number of sides, is a curve of constant ...