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The Johnson graph J(n,k) has vertices given by the k-subsets of {1,...,n}, with two vertices connected iff their intersection has size k-1. Special classes are summarized in ...

Let R(z) be a rational function R(z)=(P(z))/(Q(z)), (1) where z in C^*, C^* is the Riemann sphere C union {infty}, and P and Q are polynomials without common divisors. The ...

A branch of mathematics which brings together ideas from algebraic geometry, linear algebra, and number theory. In general, there are two main types of K-theory: topological ...

A theorem outlined by Kolmogorov (1954) which was subsequently proved in the 1960s by Arnol'd (1963) and Moser (1962; Tabor 1989, p. 105). It gives conditions under which ...

A 4-state two-dimensional Turing machine invented in the 1980s. The ant starts out on a grid containing black and white cells, and then follows the following set of rules. 1. ...

Let z=re^(itheta)=x+iy be a complex number, then inequality |(zexp(sqrt(1-z^2)))/(1+sqrt(1-z^2))|<=1 (1) holds in the lens-shaped region illustrated above. Written explicitly ...

Lorentzian n-space is the inner product space consisting of the vector space R^n together with the n-dimensional Lorentzian inner product. In the event that the (1,n-1) ...

Macdonald's plane partition conjecture proposes a formula for the number of cyclically symmetric plane partitions (CSPPs) of a given integer whose Ferrers diagrams fit inside ...

Marion's theorem (Mathematics Teacher 1993, Maushard 1994, Morgan 1994) states that the area of the central hexagonal region determined by trisection of each side of a ...

Roughly speaking, a matroid is a finite set together with a generalization of a concept from linear algebra that satisfies a natural set of properties for that concept. For ...