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The theory of analyzing a decision between a collection of alternatives made by a collection of n voters with separate opinions. Any choice for the entire group should ...

A fundamental structural result in extremal graph theory due to Szemerédi (1978). The regularity lemma essentially says that every graph can be well-approximated by the union ...

Let L be a nontrivial bounded lattice (or a complemented lattice, etc.). Then L is a tight lattice if every proper tolerance rho of L satisfies (0,a) in rho=>a=0, and dually ...

Let G be a graph and S a subgraph of G. Let the number of odd components in G-S be denoted S^', and |S| the number of graph vertices of S. The condition |S|>=S^' for every ...

Vizing's theorem states that a graph can be edge-colored in either Delta or Delta+1 colors, where Delta is the maximum vertex degree of the graph. This partitions graphs into ...

A q-analog of the gamma function defined by Gamma_q(x)=((q;q)_infty)/((q^x;q)_infty)(1-q)^(1-x), (1) where (x,q)_infty is a q-Pochhammer symbol (Koepf 1998, p. 26; Koekoek ...

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).

A q-analog of Zeilberger's algorithm.

First published in Riemann's groundbreaking 1859 paper (Riemann 1859), the Riemann hypothesis is a deep mathematical conjecture which states that the nontrivial Riemann zeta ...

Angle trisection is the division of an arbitrary angle into three equal angles. It was one of the three geometric problems of antiquity for which solutions using only compass ...