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A busy beaver is an n-state, 2-color Turing machine which writes a maximum number Sigma(n) of 1s before halting (Rado 1962; Lin and Rado 1965; Shallit 1998). Alternatively, ...

The Delannoy numbers D(a,b) are the number of lattice paths from (0,0) to (b,a) in which only east (1, 0), north (0, 1), and northeast (1, 1) steps are allowed (i.e., ->, ^, ...

According to Euler's rotation theorem, any rotation may be described using three angles. If the rotations are written in terms of rotation matrices D, C, and B, then a ...

A finite field is a field with a finite field order (i.e., number of elements), also called a Galois field. The order of a finite field is always a prime or a power of a ...

The class of all regular sequences of particularly well-behaved functions equivalent to a given regular sequence. A distribution is sometimes also called a "generalized ...

The word "graph" has (at least) two meanings in mathematics. In elementary mathematics, "graph" refers to a function graph or "graph of a function," i.e., a plot. In a ...

The Hanoi graph H_n corresponding to the allowed moves in the tower of Hanoi problem. The above figure shows the Hanoi graphs for small n. The Hanoi graph H_n can be ...

To predict the result of a measurement requires (1) a model of the system under investigation, and (2) a physical theory linking the parameters of the model to the parameters ...

The term limit comes about relative to a number of topics from several different branches of mathematics. A sequence x_1,x_2,... of elements in a topological space X is said ...

Linear algebra is the study of linear sets of equations and their transformation properties. Linear algebra allows the analysis of rotations in space, least squares fitting, ...