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Sociable numbers are numbers that result in a periodic aliquot sequence, where an aliquot sequence is the sequence of numbers obtained by repeatedly applying the restricted ...

A correspondence between a permutation and a pair of Young tableaux.

A function element is an ordered pair (f,U) where U is a disk D(Z_0,r) and f is an analytic function defined on U. If W is an open set, then a function element in W is a pair ...

A change in a knot projection such that a pair of oppositely oriented strands are passed through another pair of oppositely oriented strands.

Every continuous map f:S^n->R^n must identify a pair of antipodal points.

The map H_n(X,A)->H_(n-1)(A) appearing in the long exact sequence of a pair axiom.

An operator L^~ is said to be linear if, for every pair of functions f and g and scalar t, L^~(f+g)=L^~f+L^~g and L^~(tf)=tL^~f.

A pair of matrices ND^(-1) or D^(-1)N, where N is the matrix numerator and D is the denominator.

Complete digraphs are digraphs in which every pair of nodes is connected by a bidirectional edge.

If a sphere is covered by three closed sets, then one of them must contain a pair of antipodal points.