Displaying similar documents to “On conformal representations of the interior of an ellipse.”

A combinatorial proof of a result for permutation pairs

Toufik Mansour, Mark Shattuck (2012)

Open Mathematics


In this paper, a direct combinatorial proof is given of a result on permutation pairs originally due to Carlitz, Scoville, and Vaughan and later extended. It concerns showing that the series expansion of the reciprocal of a certain multiply exponential generating function has positive integer coefficients. The arguments may then be applied to related problems, one of which concerns the reciprocal of the exponential series for Fibonacci numbers.

A duality for isotropic median algebras

Miroslav Ploščica (1992)

Commentationes Mathematicae Universitatis Carolinae


We establish categorical dualities between varieties of isotropic median algebras and suitable categories of operational and relational topological structures. We follow a general duality theory of B.A. Davey and H. Werner. The duality results are used to describe free isotropic median algebras. If the number of free generators is less than five, the description is detailed.