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A relation "<=" is called a preorder (or quasiorder) on a set S if it satisfies: 1. Reflexivity: a<=a for all a in S. 2. Transitivity: a<=b and b<=c implies a<=c. A preorder ...

A partially ordered set (or poset) is a set taken together with a partial order on it. Formally, a partially ordered set is defined as an ordered pair P=(X,<=), where X is ...

The partial order width of a set P is equal to the minimum number of chains needed to cover P. Equivalently, if a set P of ab+1 elements is partially ordered, then P contains ...

Young's lattice Y_p is the partial order of partitions contained within a partition p ordered by containment (Stanton and White 1986; Skiena 1990, p. 77).

A total order (or "totally ordered set," or "linearly ordered set") is a set plus a relation on the set (called a total order) that satisfies the conditions for a partial ...

A second-order partial differential equation of the form Hr+2Ks+Lt+M+N(rt-s^2)=0, (1) where H, K, L, M, and N are functions of x, y, z, p, and q, and r, s, t, p, and q are ...

The transitive reflexive reduction of a partial order. An element z of a partially ordered set (X,<=) covers another element x provided that there exists no third element y ...

Let any finite or infinite set of points having no finite limit point be prescribed and associate with each of its points a principal part, i.e., a rational function of the ...

The ordinary Onsager equation is the sixth-order ordinary differential equation (d^3)/(dx^3)[e^x(d^2)/(dx^2)(e^x(dy)/(dx))]=f(x) (Vicelli 1983; Zwillinger 1997, p. 128), ...

The number of elements of a group in a given conjugacy class.