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The theta series of a lattice is the generating function for the number of vectors with norm n in the lattice. Theta series for a number of lattices are implemented in the ...

In general, a topological index, sometimes also known as a graph-theoretic index, is a numerical invariant of a chemical graph (Plavšić et al. 1993). Particular topological ...

The number of colors sufficient for map coloring on a surface of genus g is given by the Heawood conjecture, chi(g)=|_1/2(7+sqrt(48g+1))_|, where |_x_| is the floor function. ...

Triangle geometry is the study of the properties of triangles, including associated triangle centers, triangle lines, central circles, triangle cubics, and many others. These ...

A planar graph G is said to be triangulated (also called maximal planar) if the addition of any edge to G results in a nonplanar graph. If the special cases of the triangle ...

van der Waerden's theorem is a theorem about the existence of arithmetic progressions in sets. The theorem can be stated in four equivalent forms. 1. If N=C_1 union C_2 union ...

An xyz embedding, also called an "xyz drawing," is a three-dimensional embedding such that every axis-parallel line contains either zero or two vertices. Such an embedding is ...

Let {f_n} and {a_n} be sequences with f_n>=f_(n+1)>0 for n=1, 2, ..., then |sum_(n=1)^ma_nf_n|<=Af_1, where A=max{|a_1|,|a_1+a_2|,...,|a_1+a_2+...+a_m|}.

The absolute difference of two numbers n_1 and n_2 is |n_1-n_2|, where the minus sign denotes subtraction and |x| denotes the absolute value.

An additive function is an arithmetic function such that whenever positive integers a and b are relatively prime, f(ab)=f(a)+f(b). An example of an additive function is ...