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Let there be m doctors and n<=m patients, and let all mn possible combinations of examinations of patients by doctors take place. Then what is the minimum number of surgical ...

A partition {a_1,...,a_n} is called graphical if there exists a graph G having degree sequence {a_1,...,a_n}. The number of graphical partitions of length n is equal to the ...

There are (at least) two graphs associated with Horton, illustrated above. The first is a graph on 96 nodes providing a counterexample to the Tutte conjecture that every ...

An isohedron is a convex polyhedron with symmetries acting transitively on its faces with respect to the center of gravity. Every isohedron has an even number of faces ...

A direct search method of optimization that works moderately well for stochastic problems. It is based on evaluating a function at the vertices of a simplex, then iteratively ...

The Ouchi illusion, illustrated above, is an illusion named after its inventor, Japanese artist Hajime Ouchi. In this illusion, the central disk seems to float above the ...

A closed planar quadrilateral with opposite sides of equal lengths a and b, and with four right angles. A square is a degenerate rectangle with a=b. The area of the rectangle ...

A rooted graph is a graph in which one node is labeled in a special way so as to distinguish it from other nodes. The special node is called the root of the graph. The rooted ...

A correction which must be applied to the measured moments m_k obtained from normally distributed data which have been binned in order to obtain correct estimators mu^^_i for ...

As proved by Sierpiński (1960), there exist infinitely many positive odd numbers k such that k·2^n+1 is composite for every n>=1. Numbers k with this property are called ...