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The Kauffman X-polynomial, also called the normalized bracket polynomial, is a 1-variable knot polynomial denoted X (Adams 1994, p. 153), L (Kauffman 1991, p. 33), or F ...

Let [a_0;a_1,a_2,...] be the simple continued fraction of a "generic" real number, where the numbers a_i are the partial quotients. Then the Khinchin (or Khintchine) harmonic ...

A finitely generated discontinuous group of linear fractional transformations z->(az+b)/(cz+d) acting on a domain in the complex plane. The Apollonian gasket corresponds to a ...

The least genus of any Seifert surface for a given knot. The unknot is the only knot with genus 0. Usually, one denotes by g(K) the genus of the knot K. The knot genus has ...

A fractal derived from the Koch snowflake. The base curve and motif for the fractal are illustrated below. The area enclosed by pieces of the curve after the nth iteration is ...

In the field of functional analysis, the Krein-Milman theorem is a result which characterizes all (nonempty) compact convex subsets K of "sufficiently nice" topological ...

The Kuratowski reduction theorem states that very nonplanar graph contains either the utility graph UG=K_(3,3) or the pentatope graph K_5 as a graph minor. The graphs K_(3,3) ...

An attractive tiling of the square composed of two types of triangular tiles. It consists of 16 equilateral triangles and 32 15 degrees-15 degrees-150 degrees isosceles ...

A lattice automorphism is a lattice endomorphism that is also a lattice isomorphism.

A Laurent polynomial with coefficients in the field F is an algebraic object that is typically expressed in the form ...+a_(-n)t^(-n)+a_(-(n-1))t^(-(n-1))+... ...