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An unordered factorization is a factorization of a number into a product of factors where order is ignored. The following table lists the unordered factorizations of the ...

A schematic diagram used in logic theory to depict collections of sets and represent their relationships. The Venn diagrams on two and three sets are illustrated above. The ...

A vertex coloring is an assignment of labels or colors to each vertex of a graph such that no edge connects two identically colored vertices. The most common type of vertex ...

A zebra graph is a graph formed by all possible moves of a hypothetical chess piece called a "zebra" which moves analogously to a knight except that it is restricted to moves ...

Zeno's paradoxes are a set of four paradoxes dealing with counterintuitive aspects of continuous space and time. 1. Dichotomy paradox: Before an object can travel a given ...

The abc conjecture is a conjecture due to Oesterlé and Masser in 1985. It states that, for any infinitesimal epsilon>0, there exists a constant C_epsilon such that for any ...

Discrete Mathematics

Number Theory

Let Xi be the xi-function defined by Xi(iz)=1/2(z^2-1/4)pi^(-z/2-1/4)Gamma(1/2z+1/4)zeta(z+1/2). (1) Xi(z/2)/8 can be viewed as the Fourier transform of the signal ...

The q-binomial coefficient is a q-analog for the binomial coefficient, also called a Gaussian coefficient or a Gaussian polynomial. A q-binomial coefficient is given by [n; ...