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There are a great many beautiful identities involving q-series, some of which follow directly by taking the q-analog of standard combinatorial identities, e.g., the ...

The Biggs-Smith graph is cubic symmetric graph F_(102)A on 102 vertices and 153 edges that is also distance-regular with intersection array {3,2,2,2,1,1,1;1,1,1,1,1,1,3} and ...

Buffon's needle problem asks to find the probability that a needle of length l will land on a line, given a floor with equally spaced parallel lines a distance d apart. The ...

Combinatorics is the branch of mathematics studying the enumeration, combination, and permutation of sets of elements and the mathematical relations that characterize their ...

The Danzer graph is the Levi graph of the Danzer configuration (Boben et al. 2015). It has 70 vertices and 140 edges and is quartic, bipartite, self-dual, and unit-distance. ...

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 ...

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 ...

A matrix is a concise and useful way of uniquely representing and working with linear transformations. In particular, every linear transformation can be represented by a ...

Number theory is a vast and fascinating field of mathematics, sometimes called "higher arithmetic," consisting of the study of the properties of whole numbers. Primes and ...

Pascal's triangle is a number triangle with numbers arranged in staggered rows such that a_(nr)=(n!)/(r!(n-r)!)=(n; r), (1) where (n; r) is a binomial coefficient. The ...