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Let a random n×n (0,1)-matrix have entries which are 1 (with probability p) or 0 (with probability q=1-p). An s-cluster is an isolated group of s adjacent (i.e., horizontally ...

A dot plot, also called a dot chart, is a type of simple histogram-like chart used in statistics for relatively small data sets where values fall into a number of discrete ...

Due to nonlinearities in weather processes, a butterfly flapping its wings in Tahiti can, in theory, produce a tornado in Kansas. This strong dependence of outcomes on very ...

An orientation of an undirected graph G is an assignment of exactly one direction to each of the edges of G. Only connected, bridgeless graphs can have a strong orientation ...

A prime partition of a positive integer n>=2 is a set of primes p_i which sum to n. For example, there are three prime partitions of 7 since 7=7=2+5=2+2+3. The number of ...

A wide variety of large numbers crop up in mathematics. Some are contrived, but some actually arise in proofs. Often, it is possible to prove existence theorems by deriving ...

The icosahedral graph is the Platonic graph whose nodes have the connectivity of the regular icosahedron, as well as the great dodecahedron, great icosahedron Jessen's ...

Heule graphs are a set of unit-distance graphs with chromatic number five derived by Marijn Heule in April 2018 to July 2918 from the 1581-vertex de Grey Graph (Heule 2018). ...

Given a real number x, find the powers of a base b that will shift the digits of x a number of places n to the left. This is equivalent to solving b^x=b^nx (1) or x=n+log_bx. ...

A prime link is a link that cannot be represented as a knot sum of other links. Doll and Hoste (1991) list polynomials for oriented links of nine or fewer crossings, and ...