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Given two positive integers n and k, the bipartite Kneser graph H(n,k) is the graph whose two bipartite sets of vertices represent the k-subsets and (n-k)-subsets of ...

It is thought that the totient valence function N_phi(m)>=2, i.e., if there is an n such that phi(n)=m, then there are at least two solutions n. This assertion is called ...

Wirsing (1974) showed, among other results, that if F_n(x) is the Gauss-Kuzmin distribution, then lim_(n->infty)(F_n(x)-lg(1+x))/((-lambda)^n)=Psi(x), (1) where ...

Square line picking is the selection of pairs of points (corresponding to endpoints of a line segment) randomly placed inside a square. n random line segments can be picked ...

The arithmetic-geometric energy of a graph is defined as the graph energy of its arithmetic-geometric matrix, i.e., the sum of the absolute values of the eigenvalues of its ...

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 ...

Polynomials s_k(x;lambda) which form a Sheffer sequence with g(t) = 1+e^(lambdat) (1) f(t) = e^t-1 (2) and have generating function ...

The classification theorem of finite simple groups, also known as the "enormous theorem," which states that the finite simple groups can be classified completely into 1. ...

An oriented graph is a directed graph having no symmetric pair of directed edges. A complete oriented graph is called a tournament. The numbers of oriented graphs on n=1, 2, ...

The Poisson-Charlier polynomials c_k(x;a) form a Sheffer sequence with g(t) = e^(a(e^t-1)) (1) f(t) = a(e^t-1), (2) giving the generating function ...