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A group representation of a group G on a vector space V can be restricted to a subgroup H. For example, the symmetric group on three letters has a representation phi on R^2 ...

The function given by CK_n(x)=cos(nxcos^(-1)x), where n is an integer and -1<x<1.

The G-transform of a function f(x) is defined by the integral (Gf)(x)=(G_(pq)^(mn)|(a_p); (b_q)|f(t))(x) (1) =1/(2pii)int_sigmaGamma[(b_m)+s, 1-(a_n)-s; (a_p^(n+1))+s, ...

An operator U satisfying U^|U = 1 (1) UU^| = 1, (2) where U^| is the adjoint.

An alternating sign matrix is a matrix of 0s, 1s, and -1s in which the entries in each row or column sum to 1 and the nonzero entries in each row and column alternate in ...

The point in the plane with Cartesian coordinates (1, 1).

The Haferman carpet is the beautiful fractal constructed using string rewriting beginning with a cell [1] and iterating the rules {0->[1 1 1; 1 1 1; 1 1 1],1->[0 1 0; 1 0 1; ...

The Sally sequence gives the sequence of lengths of the repetitions which are avoided in the Linus sequence. The first few terms are 0, 1, 1, 2, 1, 3, 1, 1, 3, 2, 1, 6, 3, 2, ...

Three types of n×n matrices can be obtained by writing Pascal's triangle as a lower triangular matrix and truncating appropriately: a symmetric matrix S_n with (S)_(ij)=(i+j; ...

Consider the number of sequences that can be formed from permutations of a set of elements such that each partial sum is nonnegative. The number of sequences with nonnegative ...