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A number of attractive 5-compounds of the regular icosahedron can be constructed. The compounds illustrated above will be implemented in a future version of the Wolfram ...

A number of attractive 6-compounds of the regular icosahedron can be constructed. The compounds illustrated above will be implemented in a future version of the Wolfram ...

Two sets A and B are said to be independent if their intersection A intersection B=emptyset, where emptyset is the empty set. For example, {A,B,C} and {D,E} are independent, ...

The intensity measure mu of a point process X relative to a Borel set B subset R^d is defined to be the expected number of points of X falling in B. Symbolically, ...

The sum I over all internal (circular) nodes of the paths from the root of an extended binary tree to each node. For example, in the tree above, the internal path length is ...

Let S(T) be the group of symmetries which map a monohedral tiling T onto itself. The transitivity class of a given tile T is then the collection of all tiles to which T can ...

Two graphs which contain the same number of graph vertices connected in the same way are said to be isomorphic. Formally, two graphs G and H with graph vertices ...

The Jacobsthal polynomials are the W-polynomial obtained by setting p(x)=1 and q(x)=2x in the Lucas polynomial sequence. The first few Jacobsthal polynomials are J_1(x) = 1 ...

For an algebraic curve, the total number of groups of a g_N^r consisting in a point of multiplicity k_1, one of multiplicity k_2, ..., one of multiplicity k_rho, where sumk_i ...

A framework is called "just rigid" if it is rigid, but ceases to be so when any single bar is removed. Lamb (1928, pp. 93-94) proved that a necessary (but not sufficient) ...