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Rule 60 is one of the elementary cellular automaton rules introduced by Stephen Wolfram in 1983 (Wolfram 1983, 2002). It specifies the next color in a cell, depending on its ...

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 ...

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 ...

Given two positive integers n and k, the bipartite Kneser graph H(n,k) is the graph whose two bipartite sets of vertices represent the k-subsets and (n-k)-subsets of ...

The Engel expansion, also called the Egyptian product, of a positive real number x is the unique increasing sequence {a_1,a_2,...} of positive integers a_i such that ...

An Euler brick is a cuboid that possesses integer edges a>b>c and face diagonals d_(ab) = sqrt(a^2+b^2) (1) d_(ac) = sqrt(a^2+c^2) (2) d_(bc) = sqrt(b^2+c^2). (3) If the ...

A Fermat pseudoprime to a base a, written psp(a), is a composite number n such that a^(n-1)=1 (mod n), i.e., it satisfies Fermat's little theorem. Sometimes the requirement ...

Gaussian primes are Gaussian integers z=a+bi satisfying one of the following properties. 1. If both a and b are nonzero then, a+bi is a Gaussian prime iff a^2+b^2 is an ...

Given a rectangle having sides in the ratio 1:phi, the golden ratio phi is defined such that partitioning the original rectangle into a square and new rectangle results in a ...

The set of graph eigenvalues of the adjacency matrix is called the spectrum of the graph. (But note that in physics, the eigenvalues of the Laplacian matrix of a graph are ...