Enumerations of Permutations by Circular Descent Sets

Details Enumerations of Permutations by Circular Descent Sets Enumerations of Permutations by Circular Descent Sets

2008-06-03

arxiv.org/abs/0806.0433v2

Mathematics

Combinatorics

Scientific paper

The circular descent of a permutation $\sigma$ is a set $\{\sigma(i)\mid \sigma(i)>\sigma(i+1)\}$. In this paper, we focus on the enumerations of permutations by the circular descent set. Let $cdes_n(S)$ be the number of permutations of length $n$ which have the circular descent set $S$. We derive the explicit formula for $cdes_n(S)$. We describe a class of generating binary trees $T_k $ with weights. We find that the number of permutations in the set $CDES_n(S)$ corresponds to the weights of $T_k$. As a application of the main results in this paper, we also give the enumeration of permutation tableaux according to their shape.

Affiliated with

Also associated with

No associations

Rating

Enumerations of Permutations by Circular Descent Sets 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 Enumerations of Permutations by Circular Descent Sets, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Enumerations of Permutations by Circular Descent Sets will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-194819