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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; ...

The number of ways a set of n elements can be partitioned into nonempty subsets is called a Bell number and is denoted B_n (not to be confused with the Bernoulli number, ...

The chromatic polynomial pi_G(z) of an undirected graph G, also denoted C(G;z) (Biggs 1973, p. 106) and P(G,x) (Godsil and Royle 2001, p. 358), is a polynomial which encodes ...

Determinants are mathematical objects that are very useful in the analysis and solution of systems of linear equations. As shown by Cramer's rule, a nonhomogeneous system of ...

A die (plural "dice") is a solid with markings on each of its faces. The faces are usually all the same shape, making Platonic solids and Archimedean duals the obvious ...

The number of digits D in an integer n is the number of numbers in some base (usually 10) required to represent it. The numbers 1 to 9 are therefore single digits, while the ...

An Egyptian fraction is a sum of positive (usually) distinct unit fractions. The famous Rhind papyrus, dated to around 1650 BC contains a table of representations of 2/n as ...