Search Results for ""

A group action G×X->X is called free if, for all x in X, gx=x implies g=I (i.e., only the identity element fixes any x). In other words, G×X->X is free if the map G×X->X×X ...

A homogeneous space M is a space with a transitive group action by a Lie group. Because a transitive group action implies that there is only one group orbit, M is isomorphic ...

A Steiner system S(t,k,v) is a set X of v points, and a collection of subsets of X of size k (called blocks), such that any t points of X are in exactly one of the blocks. ...

The Szekeres snark was the fifth snark discovered, illustrated above. It has 50 vertices and edge chromatic number 4.

The Celmins-Swart snarks are the two snarks on 26 vertices and 39 edges illustrated above. They are implemented in the Wolfram Language as GraphData["CelminsSwartSnark1"] and ...

A matching is a maximum matching iff it contains no augmenting path.

A fork of a tree T is a node of T which is the endpoint of two or more branches.

The number N_d^((b))(n) of digits d in the base-b representation of a number n is called the b-ary digit count for d. The digit count is implemented in the Wolfram Language ...

The Poincaré hyperbolic disk is a two-dimensional space having hyperbolic geometry defined as the disk {x in R^2:|x|<1}, with hyperbolic metric ...

The Sobolev embedding theorem is a result in functional analysis which proves that certain Sobolev spaces W^(k,p)(Omega) can be embedded in various spaces including ...