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In the early 1950s, Ernst Straus asked 1. Is every region illuminable from every point in the region? 2. Is every region illuminable from at least one point in the region? ...

A Laman graph is a graph satisfying Laman's theorem. In other words, it is a graph G have exactly 2n-3 graph edges, where n is the number of graph vertices in G and for which ...

In the fields of functional and harmonic analysis, the Littlewood-Paley decomposition is a particular way of decomposing the phase plane which takes a single function and ...

Long multiplication is the method of multiplication that is commonly taught to elementary school students throughout the world. It can be used on two numbers of arbitrarily ...

Macdonald's constant term conjectures are related to root systems of Lie algebras (Macdonald 1982, Andrews 1986). They can be regarded as generalizations of Dyson's ...

An independent edge set, also called a matching, of a graph G is a subset of the edges such that no two edges in the subset share a vertex in G. A maximum independent edge ...

A maze, also known as a labyrinth, as is a set of passages (with impermeable walls). The goal of the maze is to start at one given point and find a path through the passages ...

A function f is said to be an entire modular form of weight k if it satisfies 1. f is analytic in the upper half-plane H, 2. f((atau+b)/(ctau+d))=(ctau+d)^kf(tau) whenever [a ...

A Diophantine problem (i.e., one whose solution must be given in terms of integers) which seeks a solution to the following problem. Given n men and a pile of coconuts, each ...

The Petersen family of graphs, not to be confused with generalized Petersen graphs, are a set of seven graphs obtained from the Petersen graph (or complete graph K_6) by del ...