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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 ...

A triangular grid, also called an isometric grid (Gardner 1986, pp. 209-210), is a grid formed by tiling the plane regularly with equilateral triangles.

A polynomial is called unimodal if the sequence of its coefficients is unimodal. If P(x) is log-convex and Q(x) is unimodal, then P(x)Q(x) is unimodal.

A unimodal sequence is a finite sequence that first increases and then decreases. A sequence {s_1,s_2,...,s_n} is unimodal if there exists a t such that s_1<=s_2<=...<=s_t ...

Sociable numbers computed using the analog of the restricted divisor function s^*(n) in which only unitary divisors are included.

The study of valuations which simplifies class field theory and the theory of function fields.

A knot which is not a tame knot.

One name for the figure used by Euclid to prove the Pythagorean theorem.

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).

The partial differential equation ((partial^2)/(partialt^2)-(partial^2)/(partialx^2))((u_(xy))/u)+2(u^2)_(xt)=0.