Mathematics – Combinatorics
Scientific paper
2007-10-26
Mathematics
Combinatorics
5 pages; 3 figures
Scientific paper
In this paper we prove a duality between $k$-noncrossing partitions over $[n]=\{1,...,n\}$ and $k$-noncrossing braids over $[n-1]$. This duality is derived directly via (generalized) vacillating tableaux which are in correspondence to tangled-diagrams \cite{Reidys:07vac}. We give a combinatorial interpretation of the bijection in terms of the contraction of arcs of tangled-diagrams. Furthermore it induces by restriction a bijection between $k$-noncrossing, 2-regular partitions over $[n]$ and $k$-noncrossing braids without isolated points over $[n-1]$. Since braids without isolated points correspond to enhanced partitions this allows, using the results of \cite{MIRXIN}, to enumerate 2-regular, 3-noncrossing partitions.
Jin Emma Y.
Qin Jing
Reidys Christian M.
No associations
LandOfFree
On $k$-noncrossing partitions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On $k$-noncrossing partitions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On $k$-noncrossing partitions will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-191303