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A proper ideal I of a ring R is called semiprime if, whenever J^n subset I for an ideal J of R and some positive integer, then J subset I. In other words, the quotient ring ...

A transposition graph G_n is a graph whose nodes correspond to permutations and edges to permutations that differ by exactly one transposition (Skiena 1990, p. 9, Clark ...

The twist of a ribbon measures how much it twists around its axis and is defined as the integral of the incremental twist around the ribbon. A formula for the twist is given ...

A graph for which the relations between pairs of vertices are symmetric, so that each edge has no directional character (as opposed to a directed graph). Unless otherwise ...

An arithmetic function is a function f(n) defined for all n in N, usually taken to be complex-valued, so that f:N->C (Jones and Jones 1998, p. 143). An alternative definition ...

As a part of the study of Waring's problem, it is known that every positive integer is a sum of no more than 9 positive cubes (g(3)=9), that every "sufficiently large" ...

A complete oriented graph (Skiena 1990, p. 175), i.e., a graph in which every pair of nodes is connected by a single uniquely directed edge. The first and second 3-node ...

Closed forms are known for the sums of reciprocals of even-indexed Fibonacci numbers P_F^((e)) = sum_(n=1)^(infty)1/(F_(2n)) (1) = ...

An Egyptian fraction is a sum of positive (usually) distinct unit fractions. The famous Rhind papyrus, dated to around 1650 BC contains a table of representations of 2/n as ...

A two-dimensional grid graph, also known as a rectangular grid graph or two-dimensional lattice graph (e.g., Acharya and Gill 1981), is an m×n lattice graph that is the graph ...