# Crossings and nesting in tangled-diagrams - Mathematics > Combinatorics

Crossings and nesting in tangled-diagrams - Mathematics > Combinatorics - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

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.

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

Fuente: https://arxiv.org/