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Let N steps of equal length be taken along a line. Let p be the probability of taking a step to the right, q the probability of taking a step to the left, n_1 the number of ...

There are a number of hypotraceable and hypohamiltonian graphs associated with Carsten Thomassen. These graphs, illustrated above, are implemented in the Wolfram Language as ...

An almost integer is a number that is very close to an integer. Near-solutions to Fermat's last theorem provide a number of high-profile almost integers. In the season 7, ...

The Gauss-Kuzmin distribution is the distribution of occurrences of a positive integer k in the continued fraction of a random (or "generic") real number. Consider xi_n ...

The Hall-Janko graph, also known as the Hall-Janko-Wales graph, is a strongly regular graph on 100 nodes with parameters (nu,k,lambda,mu)=(100,36,14,12). It is also a ...

Let s_k be the number of independent vertex sets of cardinality k in a graph G. The polynomial I(x)=sum_(k=0)^(alpha(G))s_kx^k, (1) where alpha(G) is the independence number, ...

Let lambda_(m,n) be Chebyshev constants. Schönhage (1973) proved that lim_(n->infty)(lambda_(0,n))^(1/n)=1/3. (1) It was conjectured that the number ...

A polygon can be defined (as illustrated above) as a geometric object "consisting of a number of points (called vertices) and an equal number of line segments (called sides), ...

The term "snark" was first popularized by Gardner (1976) as a class of minimal cubic graphs with edge chromatic number 4 and certain connectivity requirements. (By Vizing's ...

An amicable pair (m,n) consists of two integers m,n for which the sum of proper divisors (the divisors excluding the number itself) of one number equals the other. Amicable ...