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A symplectic form on a smooth manifold M is a smooth closed 2-form omega on M which is nondegenerate such that at every point m, the alternating bilinear form omega_m on the ...

When a Young tableau is constructed using the so-called insertion algorithm, an element starts in some position on the first row, from which it may later be bumped. In ...

An n×n array of the integers from 1 to n^2 such that the difference between any one integer and its neighbor (horizontally, vertically, or diagonally, without wrapping ...

A relation on a totally ordered set.

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.