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How can a delegation of six regiments, each of which sends a colonel, a lieutenant-colonel, a major, a captain, a lieutenant, and a sub-lieutenant be arranged in a regular ...

A Lie algebra is a vector space g with a Lie bracket [X,Y], satisfying the Jacobi identity. Hence any element X gives a linear transformation given by ad(X)(Y)=[X,Y], (1) ...

Define an antipode of a given graph vertex v_i as a vertex v_j at greatest possible graph distance from v_i. Then an antipodal graph is a connected graph in which each vertex ...

A number n is called a barrier of a number-theoretic function f(m) if, for all m<n, m+f(m)<=n. Neither the totient function phi(n) nor the divisor function sigma(n) has a ...

The binary logarithm log_2x is the logarithm to base 2. The notation lgx is sometimes used to denote this function in number theoretic literature. However, because Russian ...

Binet's formula is an equation which gives the nth Fibonacci number as a difference of positive and negative nth powers of the golden ratio phi. It can be written as F_n = ...

A braid index is the least number of strings needed to make a closed braid representation of a link. The braid index is equal to the least number of Seifert circles in any ...

The area of the shadow of a body on a plane, also called the "outer quermass."

Given a permutation {p_1,p_2,...,p_n} of {1,...,n}, the bumping algorithm constructs a standard Young tableau by inserting the p_i one by one into an already constructed ...

Letting Lk be the linking number of the two components of a ribbon, Tw be the twist, and Wr be the writhe, then Lk(K)=Tw(K)+Wr(K). (Adams 1994, p. 187).