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The Kaprekar routine is an algorithm discovered in 1949 by D. R. Kaprekar for 4-digit numbers, but which can be generalized to k-digit numbers. To apply the Kaprekar routine ...

An algorithm for multiplying two 32-bit integers modulo a 32-bit constant without using any intermediates larger than 32 bits. It is also useful in certain types of random ...

An extended rooted binary tree satisfying the following conditions: 1. Every node has two children, each colored either red or black. 2. Every tree leaf node is colored ...

A topological space, also called an abstract topological space, is a set X together with a collection of open subsets T that satisfies the four conditions: 1. The empty set ...

The associahedron is the n-dimensional generalization of the pentagon. It was discovered by Stasheff in 1963 and it is also known as the Stasheff polytope. The number of ...

A braid index is the least number of strings needed to make a closed braid representation of a link. The braid index is equal to the least number of Seifert circles in any ...

A Dyck path is a staircase walk from (0,0) to (n,n) that lies strictly below (but may touch) the diagonal y=x. The number of Dyck paths of order n is given by the Catalan ...

An edge coloring of a graph G is a coloring of the edges of G such that adjacent edges (or the edges bounding different regions) receive different colors. An edge coloring ...

A polyomino-like object made by attaching squares joined either at sides or corners. Because neighboring squares can be in relation to one another as kings may move on a ...

A finite or infinite square matrix with rational entries. (If the matrix is infinite, all but a finite number of entries in each row must be 0.) The sum or product of two ...