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A run is a sequence of more than one consecutive identical outcomes, also known as a clump. Let R_p(r,n) be the probability that a run of r or more consecutive heads appears ...

The Dedekind eta function is defined over the upper half-plane H={tau:I[tau]>0} by eta(tau) = q^_^(1/24)(q^_)_infty (1) = q^_^(1/24)product_(k=1)^(infty)(1-q^_^k) (2) = ...

The Folkman graph is a semisymmetric graph that has the minimum possible number of nodes (20) (Skiena 1990, p. 186). It is implemented in the Wolfram Language as ...

A permutation cycle is a subset of a permutation whose elements trade places with one another. Permutations cycles are called "orbits" by Comtet (1974, p. 256). For example, ...

The Andrews-Gordon identity (Andrews 1974) is the analytic counterpart of Gordon's combinatorial generalization of the Rogers-Ramanujan identities (Gordon 1961). It has a ...

Two lines PQ and RS are said to be antiparallel with respect to the sides of an angle A if they make the same angle in the opposite senses with the bisector of that angle. If ...

An articulation vertex of a connected graph, also called a cut-vertex (Harary 1994, p. 26; West 2000; Gross and Yellen 2006) or "cutpoint" (Harary 1994, p. 26), is a vertex ...

The sequence a(n) given by the exponents of the highest power of 2 dividing n, i.e., the number of trailing 0s in the binary representation of n. For n=1, 2, ..., the first ...

A Bland-Altman plot is a data plotting method which simultaneously presents data sets from two different tests in a way that allows for easier determination of whether the ...

Consider n strings, each oriented vertically from a lower to an upper "bar." If this is the least number of strings needed to make a closed braid representation of a link, n ...