Search Results for ""

The vertex count of a graph g, commonly denoted V(g) or |g|, is the number of vertices in g. In other words, it is the cardinality of the vertex set. The vertex count of a ...

Schur (1916) proved that no matter how the set of positive integers less than or equal to |_n!e_| (where |_x_| is the floor function) is partitioned into n classes, one class ...

An integer n is p-balanced for p a prime if, among all nonzero binomial coefficients (n; k) for k=0, ..., n (mod p), there are equal numbers of quadratic residues and ...

Let a graph G=(V,E) be defined on vertex set V and edge set E. Then a construction sequence (or c-sequence) for G is a linear order on V union E in which each edge appears ...

The maximum number of pieces into which a cylinder can be divided by n oblique cuts is given by f(n) = (n+1; 3)+n+1 (1) = 1/6(n+1)(n^2-n+6) (2) = 1/6(n^3+5n+6), (3) where (a; ...

Decimal is the base-10 notational system for representing real numbers. The expression of a number using the decimal system is called its decimal expansion, examples of which ...

A radical integer is a number obtained by closing the integers under addition, multiplication, subtraction, and root extraction. An example of such a number is RadicalBox[7, ...

Rubik's Clock is a puzzle consisting of 18 small clocks, 14 of which are independent, each of which may be set to any 12-hour position. There are therefore 12^(14) possible ...

A weakly perfect graph is a graph for which omega(G)=chi(G) (without any requirement that this condition also hold on induced subgraphs, which is required for a graph to be ...

Van der Corput sequences are a means of generating sequences of points that are maximally self-avoiding (a.k.a. quasirandom sequences). In the one-dimensional case, the ...