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Abstract: A tangled-diagram over $n=\{1,

.,n\}$ is a graph of degree less than twowhose vertices $1,

.,n$ are arranged in a horizontal line and whose arcs aredrawn in the upper halfplane with a particular notion of crossings andnestings. Generalizing the construction of Chen {\it et.al.} we prove abijection between generalized vacillating tableaux with less than $k$ rows and$k$-noncrossing tangled-diagrams and study their crossings and nestings. Weshow that the number of $k$-noncrossing and $k$-nonnesting tangled-diagrams areequal and enumerate tangled-diagrams.



Author: William Y. C. Chen, Jing Qin, Christian M. Reidys

Source: https://arxiv.org/



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