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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 k-factor of a graph is a k-regular subgraph of order n. k-factors are a generalization of complete matchings. A perfect matching is a 1-factor (Skiena 1990, p. 244).

Given n sets of variates denoted {X_1}, ..., {X_n} , the first-order covariance matrix is defined by V_(ij)=cov(x_i,x_j)=<(x_i-mu_i)(x_j-mu_j)>, where mu_i is the mean. ...

A subgroup is a subset H of group elements of a group G that satisfies the four group requirements. It must therefore contain the identity element. "H is a subgroup of G" is ...

An integrating factor is a function by which an ordinary differential equation can be multiplied in order to make it integrable. For example, a linear first-order ordinary ...

The center of any sphere which has a contact of (at least) first-order with a curve C at a point P lies in the normal plane to C at P. The center of any sphere which has a ...

The Prelle-Singer method is a semi-decision procedure for solving nonlinear first-order ordinary differential equations of the form y^'=P(x,y)/Q(x,y), where P and Q are ...

If we expand the determinant of a matrix A using determinant expansion by minors, first in terms of the minors of order r formed from any r rows, with their complementaries, ...

A Room square (named after T. G. Room) of order n (for n even) is an arrangement in an (n-1)×(n-1) square matrix of n objects such that each cell is either empty or holds ...

The constants lambda_(m,n)=inf_(r in R_(m,n))sup_(x>=0)|e^(-x)-r(x)|, where r(x)=(p(x))/(q(x)), p and q are mth and nth order polynomials, and R_(m,n) is the set of all ...