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A fundamental structural result in extremal graph theory due to Szemerédi (1978). The regularity lemma essentially says that every graph can be well-approximated by the union ...

With n cuts of a torus of genus 1, the maximum number of pieces which can be obtained is N(n)=1/6(n^3+3n^2+8n). The first few terms are 2, 6, 13, 24, 40, 62, 91, 128, 174, ...

A product space product_(i in I)X_i is compact iff X_i is compact for all i in I. In other words, the topological product of any number of compact spaces is compact. In ...

An n-uniform tessellation is a tessellation than has n transitivity classes of vertices. The 1-uniform tessellations are sometimes known as Archimedean tessellations. The ...

The abundancy of a number n is defined as the ratio sigma(n)/n, where sigma(n) is the divisor function. For n=1, 2, ..., the first few values are 1, 3/2, 4/3, 7/4, 6/5, 2, ...

Aleph-1 is the set theory symbol aleph_1 for the smallest infinite set larger than aleph_0 (Aleph-0), which in turn is equal to the cardinal number of the set of countable ...

An Euler-Jacobi pseudoprime to a base a is an odd composite number n such that (a,n)=1 and the Jacobi symbol (a/n) satisfies (a/n)=a^((n-1)/2) (mod n) (Guy 1994; but note ...

The term "Euler function" may be used to refer to any of several functions in number theory and the theory of special functions, including 1. the totient function phi(n), ...

A radical integer is a number obtained by closing the integers under addition, multiplication, subtraction, and root extraction. An example of such a number is RadicalBox[7, ...

The sequence obtained from reversing the digits of a number n and adding the result to the original number. For n=1, 2, ..., this gives 2, 4, 6, 8, 10, 12, 14, 16, 18, 11, ...