Bijections for Baxter Families and Related Objects

Details Bijections for Baxter Families and Related Objects Bijections for Baxter Families and Related Objects

2008-03-11

arxiv.org/abs/0803.1546v1

Mathematics

Combinatorics

31 pages, 22 figures, submitted to JCTA

Scientific paper

The Baxter number can be written as $B_n = \sum_0^n \Theta_{k,n-k-1}$. These numbers have first appeared in the enumeration of so-called Baxter permutations; $B_n$ is the number of Baxter permutations of size $n$, and $\Theta_{k,l}$ is the number of Baxter permutations with $k$ descents and $l$ rises. With a series of bijections we identify several families of combinatorial objects counted by the numbers $\Theta_{k,l}$. Apart from Baxter permutations, these include plane bipolar orientations with $k+2$ vertices and $l+2$ faces, 2-orientations of planar quadrangulations with $k+2$ white and $l+2$ black vertices, certain pairs of binary trees with $k+1$ left and $l+1$ right leaves, and a family of triples of non-intersecting lattice paths. This last family allows us to determine the value of $\Theta_{k,l}$ as an application of the lemma of Gessel and Viennot. The approach also allows us to count certain other subfamilies, e.g., alternating Baxter permutations, objects with symmetries and, via a bijection with a class of plan bipolar orientations also Schnyder woods of triangulations, which are known to be in bijection with 3-orientations.

Affiliated with

Also associated with

No associations

Rating

Bijections for Baxter Families and Related Objects 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 Bijections for Baxter Families and Related Objects, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bijections for Baxter Families and Related Objects will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-285752