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A fundamental structural result in extremal graph theory due to Szemerédi (1978). The regularity lemma essentially says that every graph can be well-approximated by the union ...

A Trott constant is a real number whose decimal digits are equal to the terms of its continued fraction. The first Trott constant (OEIS A039662) was discovered by M. Trott in ...

The twin composites may be defined by analogy with the twin primes as pairs of composite numbers (n,n+2). Since all even number are trivially twin composites, it is natural ...

A graph for which the relations between pairs of vertices are symmetric, so that each edge has no directional character (as opposed to a directed graph). Unless otherwise ...

A generalized hypergeometric function _pF_q[alpha_1,alpha_2,...,alpha_p; beta_1,beta_2,...,beta_q;z] is said to be well-poised if p=q+1 and ...

(Bailey 1935, p. 25), where _7F_6(a_1,...,a_7;b_1,...,b_6) and _4F_3(a_1,...,a_4;b_1,b_2,b_3) are generalized hypergeometric functions with argument z=1 and Gamma(z) is the ...

A game played with two heaps of counters in which a player may take any number from either heap or the same number from both. The player taking the last counter wins. The rth ...

The Banach-Saks theorem is a result in functional analysis which proves the existence of a "nicely-convergent" subsequence for any sequence {f_n}={f_n}_(n in Z^*) of ...

A Ferrers diagram represents partitions as patterns of dots, with the nth row having the same number of dots as the nth term in the partition. The spelling "Ferrars" (Skiena ...

There are three theorems related to pedal circles that go under the collective title of the Fontené theorems. The first Fontené theorem lets DeltaABC be a triangle and P an ...