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The self-describing sequence consisting of "blocks" of single and double 1s and 2s, where a "block" is a single digit or pair of digits that is different from the digit (or ...

A random-connection model (RCM) is a graph-theoretic model of continuum percolation theory characterized by the existence of a stationary point process X and a non-increasing ...

An alternating knot is a knot which possesses a knot diagram in which crossings alternate between under- and overpasses. Not all knot diagrams of alternating knots need be ...

A Mersenne number is a number of the form M_n=2^n-1, (1) where n is an integer. The Mersenne numbers consist of all 1s in base-2, and are therefore binary repunits. The first ...

The Platonic solids, also called the regular solids or regular polyhedra, are convex polyhedra with equivalent faces composed of congruent convex regular polygons. There are ...

The cubical graph is the Platonic graph corresponding to the connectivity of the cube. It is isomorphic to the generalized Petersen graph GP(4,1), bipartite Kneser graph ...

The McLaughlin graph is a 112-regular graph on 275 nodes and 15400 edges that can be constructed from the Witt design. It is distance-regular with intersection array ...

The two functions theta(x) and psi(x) defined below are known as the Chebyshev functions. The function theta(x) is defined by theta(x) = sum_(k=1)^(pi(x))lnp_k (1) = ...

A connected graph is graph that is connected in the sense of a topological space, i.e., there is a path from any point to any other point in the graph. A graph that is not ...

The "15 puzzle" is a sliding square puzzle commonly (but incorrectly) attributed to Sam Loyd. However, research by Slocum and Sonneveld (2006) has revealed that Sam Loyd did ...