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Let N^* be the smallest dimension n of a hypercube such that if the lines joining all pairs of corners are two-colored for any n>=N^*, a complete graph K_4 of one color with ...

Minkowski's question mark function is the function y=?(x) defined by Minkowski for the purpose of mapping the quadratic surds in the open interval (0,1) into the rational ...

Consider a game, first proposed by Nicolaus Bernoulli, in which a player bets on how many tosses of a coin will be needed before it first turns up heads. The player pays a ...

The successive overrelaxation method (SOR) is a method of solving a linear system of equations Ax=b derived by extrapolating the Gauss-Seidel method. This extrapolation takes ...

Wang's conjecture states that if a set of tiles can tile the plane, then they can always be arranged to do so periodically (Wang 1961). The conjecture was refuted when Berger ...

The abc conjecture is a conjecture due to Oesterlé and Masser in 1985. It states that, for any infinitesimal epsilon>0, there exists a constant C_epsilon such that for any ...

A magic square is a square array of numbers consisting of the distinct positive integers 1, 2, ..., n^2 arranged such that the sum of the n numbers in any horizontal, ...

There are four strongly regular graphs with parameters (nu,k,lambda,mu)=(28,12,6,4), one of them being the triangular graph of order 8. The other three such graphs are known ...

The Delannoy numbers D(a,b) are the number of lattice paths from (0,0) to (b,a) in which only east (1, 0), north (0, 1), and northeast (1, 1) steps are allowed (i.e., ->, ^, ...

The Hall-Janko graph, also known as the Hall-Janko-Wales graph, is a strongly regular graph on 100 nodes with parameters (nu,k,lambda,mu)=(100,36,14,12). It is also a ...