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Two totally ordered sets (A,<=) and (B,<=) are order isomorphic iff there is a bijection f from A to B such that for all a_1,a_2 in A, a_1<=a_2 iff f(a_1)<=f(a_2) (Ciesielski ...

An ordering of permutations in which each two adjacent permutations differ by the transposition of two elements. For the permutations of {1,2,3} there are two listings which ...

For a partial order, the size of the longest antichain is called the width.

Given a sample of n variates X_1, ..., X_N, reorder them so that Y_1<Y_2<...<Y_N. Then Y_i is called the ith order statistic (Hogg and Craig 1970, p. 146), sometimes also ...

For a partial order, the size of the longest chain is called the length.

The set of terms of first-order logic (also known as first-order predicate calculus) is defined by the following rules: 1. A variable is a term. 2. If f is an n-place ...

Let n be a positive number having primitive roots. If g is a primitive root of n, then the numbers 1, g, g^2, ..., g^(phi(n)-1) form a reduced residue system modulo n, where ...

An element of order 2 in a group (i.e., an element A of a group such that A^2=I, where I is the identity element).

An ordinary differential equation of order n is an equation of the form F(x,y,y^',...,y^((n)))=0.

A procedure for determining the behavior of an nth order ordinary differential equation at a removable singularity without actually solving the equation. Consider ...