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CROSSINGS AND NESTINGS IN TANGLED-DIAGRAMS

By William Y. C. Chen, Jing Qin, Christian and M. Reidys

Abstract

Abstract. A tangled-diagram over [n] = {1,..., n} is a graph of degree less than two whose vertices 1,..., n are arranged in a horizontal line and whose arcs are drawn in the upper halfplane with a particular notion of crossings and nestings. Generalizing the construction of Chen et.al. we prove a bijection between generalized vacillating tableaux with less than k rows and k-noncrossing tangled-diagrams and study their crossings and nestings. We show that the number of k-noncrossing and k-nonnesting tangled-diagrams are equal and enumerate tangled-diagrams. 1

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