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Let N steps of equal length be taken along a line. Let p be the probability of taking a step to the right, q the probability of taking a step to the left, n_1 the number of ...

The value for zeta(2)=sum_(k=1)^infty1/(k^2) (1) can be found using a number of different techniques (Apostol 1983, Choe 1987, Giesy 1972, Holme 1970, Kimble 1987, Knopp and ...

The term "snark" was first popularized by Gardner (1976) as a class of minimal cubic graphs with edge chromatic number 4 and certain connectivity requirements. (By Vizing's ...

The Wiener index W, denoted w (Wiener 1947) and also known as the "path number" or Wiener number (Plavšić et al. 1993), is a graph index defined for a graph on n nodes by ...

Let x be a real number, and let R be the set of positive real numbers mu for which 0<|x-p/q|<1/(q^mu) (1) has (at most) finitely many solutions p/q for p and q integers. Then ...

A graph is said to be regular of degree r if all local degrees are the same number r. A 0-regular graph is an empty graph, a 1-regular graph consists of disconnected edges, ...

A fusene is a simple planar 2-connected graph embedded in the plane with all vertices of degree 2 or 3, all bounded faces (not necessarily regular) hexagons, and all vertices ...

Infinity, most often denoted as infty, is an unbounded quantity that is greater than every real number. The symbol infty had been used as an alternative to M (1000) in Roman ...

A labeled graph G=(V,E) is a finite series of graph vertices V with a set of graph edges E of 2-subsets of V. Given a graph vertex set V_n={1,2,...,n}, the number of ...

The negabinary representation of a number n is its representation in base -2 (i.e., base negative 2). It is therefore given by the coefficients a_na_(n-1)...a_1a_0 in n = ...