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van der Waerden's theorem is a theorem about the existence of arithmetic progressions in sets. The theorem can be stated in four equivalent forms. 1. If N=C_1 union C_2 union ...

An xyz embedding, also called an "xyz drawing," is a three-dimensional embedding such that every axis-parallel line contains either zero or two vertices. Such an embedding is ...

The number of ways a set of n elements can be partitioned into nonempty subsets is called a Bell number and is denoted B_n (not to be confused with the Bernoulli number, ...

Bouwer graphs, a term coined here for the first time, are a family of regular graphs which includes members that are symmetric but not arc-transitive. Such graphs are termed ...

A Fourier series is an expansion of a periodic function f(x) in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality relationships of ...

An n-mark Golomb ruler is a set of n distinct nonnegative integers (a_1,a_2,...,a_n), called "marks," such that the positive differences |a_i-a_j|, computed over all possible ...

The maximum leaf number l(G) of a graph G is the largest number of tree leaves in any of its spanning trees. (The corresponding smallest number of leaves is known as the ...

A theorem of fundamental importance in spectroscopy and angular momentum theory which provides both (1) an explicit form for the dependence of all matrix elements of ...

The set of roots of a polynomial f(x,y,z)=0. An algebraic surface is said to be of degree n=max(i+j+k), where n is the maximum sum of powers of all terms ...

A puzzle involving disentangling a set of rings from a looped double rod, originally used by French peasants to lock chests (Steinhaus 1999). The word "baguenaudier" means ...