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A Turing machine which, by appropriate programming using a finite length of input tape, can act as any Turing machine whatsoever. In his seminal paper, Turing himself gave ...

A regular graph that is not strongly regular is known as a weakly regular graph. There are no weakly regular simple graphs on fewer than six nodes, and the numbers on n=6, 7, ...

Yahtzee is a game played with five 6-sided dice. Players take turns rolling the dice, and trying to get certain types of rolls, each with an assigned point value, as ...

A number n with prime factorization n=product_(i=1)^rp_i^(a_i) is called k-almost prime if it has a sum of exponents sum_(i=1)^(r)a_i=k, i.e., when the prime factor ...

In most computer programs and computing environments, the precision of any calculation (even including addition) is limited by the word size of the computer, that is, by ...

The 13 Archimedean dual graphs are the skeletons of the Archimedean dual solids, illustrated above. Since they are polyhedral graphs, they are also planar. However, none of ...

A recursive primality certificate for a prime p. The certificate consists of a list of 1. A point on an elliptic curve C y^2=x^3+g_2x+g_3 (mod p) for some numbers g_2 and ...

A biplanar graph is defined as a graph that is the graph union of two planar edge-induced subgraphs. In other words, biplanar graphs are graphs with graph thickness 1 or 2 ...

A bishop graph is a graph formed from possible moves of a bishop chess piece, which may make diagonal moves of any length on a chessboard (or any other board). To form the ...

A theorem which effectively describes how lengths, areas, volumes, and generalized n-dimensional volumes (contents) are distorted by differentiable functions. In particular, ...