Search Results for ""

The number of alternating permutations for n elements is sometimes called an Euler zigzag number. Denote the number of alternating permutations on n elements for which the ...

The Eulerian number <n; k> gives the number of permutations of {1,2,...,n} having k permutation ascents (Graham et al. 1994, p. 267). Note that a slightly different ...

An event is a certain subset of a probability space. Events are therefore collections of outcomes on which probabilities have been assigned. Events are sometimes assumed to ...

The knots that make up a knot sum of a composite knot are known as factor knots (Adams 1994, p. 8).

A group action phi:G×X->X is called faithful if there are no group elements g (except the identity element) such that gx=x for all x in X. Equivalently, the map phi induces ...

Given a differential p-form q in the exterior algebra ^ ^pV^*, its envelope is the smallest subspace W such that q is in the subspace ^ ^pW^* subset ^ ^pV^*. Alternatively, W ...

Any collineation from P(V) to P(V), where V is a three-dimensional vector space, is associated with a semilinear map from V to V.

Let Pi be a permutation of n elements, and let alpha_i be the number of permutation cycles of length i in this permutation. Picking Pi at random, it turns out that ...

A method for predicting the onset of widespread chaos. It is based on the hypothesis that the dissolution of an invariant torus can be associated with the sudden change from ...

The dual polyhedron of the cubohemioctahedron U_(15) and Wenninger dual W_(78). When rendered, the octahemioctacron and hexahemioctacron appear the same.