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The Christmas stocking theorem, also known as the hockey stick theorem, states that the sum of a diagonal string of numbers in Pascal's triangle starting at the nth entry ...

Two nonisomorphic graphs are said to be chromatically equivalent (also termed "chromically equivalent by Bari 1974) if they have identical chromatic polynomials. A graph that ...

Grünbaum conjectured that for every m>1, n>2, there exists an m-regular, m-chromatic graph of girth at least n. This result is trivial for n=2 or m=2,3, but only a small ...

A problem sometimes known as Moser's circle problem asks to determine the number of pieces into which a circle is divided if n points on its circumference are joined by ...

The circle method is a method employed by Hardy, Ramanujan, and Littlewood to solve many asymptotic problems in additive number theory, particularly in deriving an asymptotic ...

A uniform distribution of points on the circumference of a circle can be obtained by picking a random real number between 0 and 2pi. Picking random points on a circle is ...

A circumhyperbola is a circumconic that is a hyperbola. A rectangular circumhyperbola always passes through the orthocenter H and has center on the nine-point circle ...

Given a set P of primes, a field K is called a class field if it is a maximal normal extension of the rationals which splits all of the primes in P, and if P is the maximal ...

The complete bipartite graph K_(1,3) is a tree known as the "claw." It is isomorphic to the star graph S_4, and is sometimes known as the Y graph (Horton and Bouwer 1991; ...

The Clebsch graph, also known as the Greenwood-Gleason graph (Read and Wilson, 1998, p. 284) and illustrated above in a number of embeddings, is a strongly regular quintic ...