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The simple process of voting leads to surprisingly counterintuitive paradoxes. For example, if three people vote for three candidates, giving the rankings A, B, C; B, C, A; ...

A theorem of fundamental importance in spectroscopy and angular momentum theory which provides both (1) an explicit form for the dependence of all matrix elements of ...

A famous perceptual illusion in which the brain switches between seeing a young girl and an old woman (or "wife" and "mother in law"). An anonymous German postcard from 1888 ...

A polynomial given by Phi_n(x)=product_(k=1)^n^'(x-zeta_k), (1) where zeta_k are the roots of unity in C given by zeta_k=e^(2piik/n) (2) and k runs over integers relatively ...

The Desargues graph is the cubic symmetric graph on 20 vertices and 30 edges illustrated above in several embeddings. It is isomorphic to the generalized Petersen graph ...

The four-color theorem states that any map in a plane can be colored using four-colors in such a way that regions sharing a common boundary (other than a single point) do not ...

An n-mark Golomb ruler is a set of n distinct nonnegative integers (a_1,a_2,...,a_n), called "marks," such that the positive differences |a_i-a_j|, computed over all possible ...

In two dimensions, there are two periodic circle packings for identical circles: square lattice and hexagonal lattice. In 1940, Fejes Tóth proved that the hexagonal lattice ...

A line graph L(G) (also called an adjoint, conjugate, covering, derivative, derived, edge, edge-to-vertex dual, interchange, representative, or theta-obrazom graph) of a ...

The Nauru graph is the name given by Eppstein (2007) to the generalized Petersen graph GP(12,5) on 24 nodes and 36 edges which is also cubic symmetric graph F_(024)A, the ...