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Stanley's theorem states that the total number of 1s that occur among all unordered partitions of a positive integer is equal to the sum of the numbers of distinct members of ...

A state diagram is a labeled directed graph together with state information that can be used to indicate that certain paths on in a system may be traversed only in a certain ...

A Steiner quadruple system is a Steiner system S(t=3,k=4,v), where S is a v-set and B is a collection of k-sets of S such that every t-subset of S is contained in exactly one ...

A special type of binary tree obtained by starting with the fractions 0/1 and 1/0 and iteratively inserting (m+m^')/(n+n^') between each two adjacent fractions m/n and ...

The sequence defined by e_0=2 and the quadratic recurrence equation e_n=1+product_(i=0)^(n-1)e_i=e_(n-1)^2-e_(n-1)+1. (1) This sequence arises in Euclid's proof that there ...

The tangent numbers, also called a zag number, and given by T_n=(2^(2n)(2^(2n)-1)|B_(2n)|)/(2n), (1) where B_n is a Bernoulli number, are numbers that can be defined either ...

For a given positive integer n, does there exist a weighted tree with n graph vertices whose paths have weights 1, 2, ..., (n; 2), where (n; 2) is a binomial coefficient? ...

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. ...