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Polycairos are polyforms obtained from the Cairo tessellation, illustrated above. The numbers of polycairos with n=1, 2, ... components are 1, 2, 5, 17, 55, 206, 781, 3099, ...

Let c=(c_1,...,c_n) be a point in C^n, then the open polydisk is defined by S={z:|z_j-c_j|<|z_j^0-c_j|} for j=1, ..., n.

The term "polyedge" has been variously proposed to refer to a polystick or a simple connected graph on n edges (Muñiz 2011), the latter of which has also been termed an ...

A function which has infinitely many derivatives at a point. If a function is not polygenic, it is monogenic.

A knot equivalent to a polygon in R^3, also called a tame knot. For a polygonal knot K, there exists a plane such that the orthogonal projection pi on it satisfies the ...

One of the symmetry groups of the Platonic solids. There are three polyhedral groups: the tetrahedral group of order 12, the octahedral group of order 24, and the icosahedral ...

An integer which is expressible in more than one way in the form x^2+Dy^2 or x^2-Dy^2 where x^2 is relatively prime to Dy^2. If the integer is expressible in only one way, it ...

The highest power in a univariate polynomial is known as its degree, or sometimes "order." For example, the polynomial P(x)=a_nx^n+...+a_2x^2+a_1x+a_0 is of degree n, denoted ...

If a polynomial P(x) has a root x=a, i.e., if P(a)=0, then x-a is a factor of P(x).

A polynomial function is a function whose values can be expressed in terms of a defining polynomial. A polynomial function of maximum degree 0 is said to be a constant ...