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sum_(1<=k<=n)(n; k)((-1)^(k-1))/(k^m)=sum_(1<=i_1<=i_2<=...<=i_m<=n)1/(i_1i_2...i_m), (1) where (n; k) is a binomial coefficient (Dilcher 1995, Flajolet and Sedgewick 1995, ...

Given any assignment of n-element sets to the n^2 locations of a square n×n array, is it always possible to find a partial Latin square? The fact that such a partial Latin ...

Each of the sets forming a direct product is said to be a direct factor. A group G is said to be a direct factor of the group G^' if G^' is isomorphic to the group direct ...

A.k.a. the pigeonhole principle. Given n boxes and m>n objects, at least one box must contain more than one object. This statement has important applications in number theory ...

The term discrete percolation is used to describe models of percolation theory whose media are discrete sets like sets of regular lattice points (e.g., bond percolation and ...

The disjoint union of two sets A and B is a binary operator that combines all distinct elements of a pair of given sets, while retaining the original set membership as a ...

A statement is in disjunctive normal form if it is a disjunction (sequence of ORs) consisting of one or more disjuncts, each of which is a conjunction (AND) of one or more ...

The disk model is the standard Boolean-Poisson model in two-dimensional continuum percolation theory. In particular, the disk model is characterized by the existence of a ...

For a connected graph G of graph diameter d, the distance-k graph G_k for k=1, ..., d is a graph with the same vertex set and having edge set consisting of the pairs of ...

A labeling phi of (the vertices) of a graph G with positive integers taken from the set {1,2,...,r} is said to be r-distinguishing if no graph automorphism of G preserves all ...