Search Results for ""

A number n is called amenable if it can be built up from integers a_1, a_2, ..., a_k by either addition or multiplication such that sum_(i=1)^na_i=product_(i=1)^na_i=n (1) ...

The rectilinear crossing number of a graph G is the minimum number of crossings in a straight line embedding of G in a plane. It is variously denoted rcr(G), cr^_(G) ...

The ratio C of the largest to smallest singular value in the singular value decomposition of a matrix. The base-b logarithm of C is an estimate of how many base-b digits are ...

A generalization of Poncelet's continuity principle made by H. Schubert in 1874-1879. The conservation of number principle asserts that the number of solutions of any ...

A number which is simultaneously a pentagonal number P_n and triangular number T_m. Such numbers exist when 1/2n(3n-1)=1/2m(m+1). (1) Completing the square gives ...

A number which is simultaneously octagonal and hexagonal. Let O_n denote the nth octagonal number and H_m the mth hexagonal number, then a number which is both octagonal and ...

The Catalan numbers on nonnegative integers n are a set of numbers that arise in tree enumeration problems of the type, "In how many ways can a regular n-gon be divided into ...

The Motzkin numbers enumerate various combinatorial objects. Donaghey and Shapiro (1977) give 14 different manifestations of these numbers. In particular, they give the ...

A sum-product number is a number n such that the sum of n's digits times the product of n's digit is n itself, for example 135=(1+3+5)(1·3·5). (1) Obviously, such a number ...

The maximum number of regions that can be created by n cuts using space division by planes, cube division by planes, cylinder cutting, etc., is given by N_(max)=1/6(n^3+5n+6) ...