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For any integers a_i with 1<=a_1<a_2<...<a_k<=n, the proportion of permutations in the symmetric group S_n whose cyclic decompositions contain no cycles of lengths a_1, a_2, ...

A term of endearment used by algebraic topologists when talking about their favorite power tools such as Abelian groups, bundles, homology groups, homotopy groups, K-theory, ...

Let p be an odd prime and b a positive integer not divisible by p. Then for each positive odd integer 2k-1<p, let r_k be r_k=(2k-1)b (mod p) with 0<r_k<p, and let t be the ...

The term in rigidity theory for the edges of a graph.

A loop of an graph is degenerate edge that joins a vertex to itself, also called a self-loop. A simple graph cannot contain any loops, but a pseudograph can contain both ...

There exists a system of distinct representatives for a family of sets S_1, S_2, ..., S_m iff the union of any k of these sets contains at least k elements for all k from 1 ...

A sequence of positive integers {a_n} such that sum1/(a_nb_n) is irrational for all integer sequences {b_n}. Erdős showed that {2^(2^n)}={1,2,4,16,256,...} (OEIS A001146) is ...

If algebraic integers alpha_1, ..., alpha_n are linearly independent over Q, then e^(alpha_1), ..., e^(alpha_n) are algebraically independent over Q. The ...

The least number of crossings that occur in any projection of a link. In general, it is difficult to find the crossing number of a given link. Knots and links are generally ...

subjMathematics:Discrete Mathematics:Graph Theory:Cliques The maximal clique polynomial C_G(x) for the graph G may be defined as the polynomial ...