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

The definition of a set by enumerating its members. An extensional definition can always be reduced to an intentional one. An extension field is sometimes also called simply ...

An operator E such that E^ap(x)=p(x+a).

A knot used to shorten a long rope.

A simple pole of an analytic function f is a pole of order one. That is, (z-z_0)f(z) is an analytic function at the pole z=z_0. Alternatively, its principal part is c/(z-z_0) ...

Consecutive Smith numbers. The first few Smith brothers are (728, 729), (2964, 2965), (3864, 3865), (4959, 4960), ... (OEIS A050219 and A050220).

Socrates is reported to have stated: "One thing I know is that I know nothing."

A submonoid is a subset of the elements of a monoid that are themselves a monoid under the same monoid operation. For example, consider the monoid formed by the nonnegative ...

An ordinary knot in three dimensions suspended in four dimensions to create a knotted 2-sphere. Suspended knots are not smooth at the poles.

A catastrophe which can occur for three control factors and one behavior axis. The swallowtail catastrophe is the universal unfolding of singularity f(x)=x^5 with codimension ...