Enumeration of symmetric arc diagrams

Enumeration of skew Ferrers diagrams

Delest, M. In this paper, we show that the generating function for skew Ferrers diagrams according to their width and area is the quotient of new basic Bessel functions. Nous montrons dans cet article que la fonction g&ntratrice des diagrammes de Ferrers gauches selon les paramktres ptrimttre et aire s'exprime en fonction du quotient des q analogues de deux fonctions de Bessel.

Symmetric Enumeration Reducibility

On the Symmetric Enumeration Degrees

A set A is symmetric enumeration (se-) reducible to a set B (A≤seB) if A is enumeration reducible to B and A is enumeration reducible to B. This reducibility gives rise to a degree structure (Dse) whose least element is the class of computable sets. We give a classification of ≤se in terms of other standard reducibilities and we show that the natural embedding of the Turing degrees (DT) into th...

Equivalence of symmetric union diagrams

Motivated by the study of ribbon knots we explore symmetric unions, a beautiful construction introduced by Kinoshita and Terasaka 50 years ago. It is easy to see that every symmetric union represents a ribbon knot, but the converse is still an open problem. Besides existence it is natural to consider the question of uniqueness. In order to attack this question we extend the usual Reidemeister m...

Enumeration of bilaterally symmetric 3-noncrossing partitions

Schützenberger’s theorem for the ordinary RSK correspondence naturally extends to Chen et. al’s correspondence for matchings and partitions. Thus the counting of bilaterally symmetric k-noncrossing partitions naturally arises as an analogue for involutions. In obtaining the analogous result for 3-noncrossing partitions, we use a different technique to develop a MAPLE package for 2-dimensional v...