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Find the minimum number f(n) of subsets in a separating family for a set of n elements, where a separating family is a set of subsets in which each pair of adjacent elements ...

A problem which is both NP (verifiable in nondeterministic polynomial time) and NP-hard (any NP-problem can be translated into this problem). Examples of NP-hard problems ...

A perfect partition is a partition of a number n whose elements uniquely generate any number 1, 2, ..., n. {1,1,...,1_()_(n)} is always a perfect partition of n, and every ...

The first Strehl identity is the binomial sum identity sum_(k=0)^n(n; k)^3=sum_(k=0)^n(n; k)^2(2k; n), (Strehl 1993, 1994; Koepf 1998, p. 55), which are the so-called Franel ...

Three point geometry is a finite geometry subject to the following four axioms: 1. There exist exactly three points. 2. Two distinct points are on exactly one line. 3. Not ...

Young's geometry is a finite geometry which satisfies the following five axioms: 1. There exists at least one line. 2. Every line of the geometry has exactly three points on ...

The Legendre transform of a sequence {c_k} is the sequence {a_k} with terms given by a_n = sum_(k=0)^(n)(n; k)(n+k; k)c_k (1) = sum_(k=0)^(n)(2k; k)(n+k; n-k)c_k, (2) where ...

A q-analog of the Saalschütz theorem due to Jackson is given by where _3phi_2 is the q-hypergeometric function (Koepf 1998, p. 40; Schilling and Warnaar 1999).

Game theory is a branch of mathematics that deals with the analysis of games (i.e., situations involving parties with conflicting interests). In addition to the mathematical ...

Given five equal disks placed symmetrically about a given center, what is the smallest radius r for which the radius of the circular area covered by the five disks is 1? The ...