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A simple directed graph is a directed graph having no multiple edges or graph loops (corresponding to a binary adjacency matrix with 0s on the diagonal). The number of simple ...

The Somos sequences are a set of related symmetrical recurrence relations which, surprisingly, always give integers. The Somos sequence of order k, or Somos-k sequence, is ...

Let X be a set of v>=3 elements together with a set B of 3-subset (triples) of X such that every 2-subset of X occurs in exactly one triple of B. Then B is called a Steiner ...

A tag system is set of rules that specifies a fixed number of elements (commonly denoted nu or beta) be removed from the beginning of a sequence and a set of elements to be ...

The mean tetrahedron volume of a tetrahedron with vertices chosen at random inside another tetrahedron of unit volume is given by V^_ = (13)/(720)-(pi^2)/(15015) (1) = ...

Given three jugs with x pints in the first, y in the second, and z in the third, obtain a desired amount in one of the vessels by completely filling up and/or emptying ...

A totalistic cellular automaton is a cellular automata in which the rules depend only on the total (or equivalently, the average) of the values of the cells in a ...

A leaf of an unrooted tree is a node of vertex degree 1. Note that for a rooted or planted tree, the root vertex is generally not considered a leaf node, whereas all other ...

In database structures, two quantities are generally of interest: the average number of comparisons required to 1. Find an existing random record, and 2. Insert a new random ...

Turmites, also called turning machines, are 2-dimensional Turing machines in which the "tape" consists of a grid of spaces that can be written and erased by an active ...