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The Motzkin numbers enumerate various combinatorial objects. Donaghey and Shapiro (1977) give 14 different manifestations of these numbers. In particular, they give the ...

A permutation, also called an "arrangement number" or "order," is a rearrangement of the elements of an ordered list S into a one-to-one correspondence with S itself. The ...

Zarankiewicz's conjecture asserts that graph crossing number for a complete bipartite graph K_(m,n) is Z(m,n)=|_n/2_||_(n-1)/2_||_m/2_||_(m-1)/2_|, (1) where |_x_| is the ...

The fast Fourier transform (FFT) is a discrete Fourier transform algorithm which reduces the number of computations needed for N points from 2N^2 to 2NlgN, where lg is the ...

The usual number of scalar operations (i.e., the total number of additions and multiplications) required to perform n×n matrix multiplication is M(n)=2n^3-n^2 (1) (i.e., n^3 ...

An integer sequence whose terms are defined in terms of number-related words in some language. For example, the following table gives the sequences of numbers having digits ...

In most computer programs and computing environments, the precision of any calculation (even including addition) is limited by the word size of the computer, that is, by ...

Let pi_(m,n)(x) denote the number of primes <=x which are congruent to n modulo m (i.e., the modular prime counting function). Then one might expect that ...

The square-triangle theorem states that any nonnegative integer can be represented as the sum of a square, an even square, and a triangular number (Sun 2005), i.e., ...

Vizing's theorem states that a graph can be edge-colored in either Delta or Delta+1 colors, where Delta is the maximum vertex degree of the graph. A graph with edge chromatic ...