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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 ...

Rule 30 is one of the elementary cellular automaton rules introduced by Stephen Wolfram in 1983 (Wolfram 1983, 2002). It specifies the next color in a cell, depending on its ...

Abstract Algebra

The Catalan numbers on nonnegative integers n are a set of numbers that arise in tree enumeration problems of the type, "In how many ways can a regular n-gon be divided into ...

The number two (2) is the second positive integer and the first prime number. It is even, and is the only even prime (the primes other than 2 are called the odd primes). The ...

A Chaitin's constant, also called a Chaitin omega number, introduced by Chaitin (1975), is the halting probability of a universal prefix-free (self-delimiting) Turing ...

Consider the recurrence equation defined by a_0=m and a_n=|_sqrt(2a_(n-1)(a_(n-1)+1))_|, (1) where |_x_| is the floor function. Graham and Pollak actually defined a_1=m, but ...

A lossless data compression algorithm which uses a small number of bits to encode common characters. Huffman coding approximates the probability for each character as a power ...

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 ...