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A group having an infinite number of elements. Some infinite groups, such as the integers or rationals, are not continuous groups.

A relation between permutations p and q that exists if there is a sequence of transpositions such that each transposition increases the number of inversions (Stanton and ...

The number of elements greater than i to the left of i in a permutation gives the ith element of the inversion vector (Skiena 1990, p. 27).

For n>=1, let u and v be integers with u>v>0 such that the Euclidean algorithm applied to u and v requires exactly n division steps and such that u is as small as possible ...

If K is a finite complex and h:|K|->|K| is a continuous map, then Lambda(h)=sum(-1)^pTr(h_*,H_p(K)/T_p(K)) is the Lefschetz number of the map h.

Data resulting from the observation of a population on a number of variables over time. Whenever observations are made more than once, the data is considered to be ...

The sequence generated by repeated application of a map. The map is said to have a closed orbit if it has a finite number of elements.

A Maurer rose is a plot of a "walk" along an n- (or 2n-) leafed rose curve in steps of a fixed number d degrees, including all cosets.

The ring of integers of a number field K, denoted O_K, is the set of algebraic integers in K, which is a ring of dimension d over Z, where d is the extension degree of K over ...

A set having the largest number k of distinct residue classes modulo m so that no subset has zero sum.