On Path diagrams and Stirling permutations

Details On Path diagrams and Stirling permutations On Path diagrams and Stirling permutations

2009-06-09

arxiv.org/abs/0906.1672v1

Mathematics

Combinatorics

16 pages, 5 figures

Scientific paper

Any ordinary permutation $\tau\in S_n$ of size $n$, written as a word $\tau=\tau_1...\tau_n$, can be locally classified according to the relative order of $\tau_j$ to its neighbours. This gives rise to four local order types called peaks (or maxima), valleys (or minima), double rises and double falls. By the correspondence between permutations and binary increasing trees the classification of permutations according to local types corresponds to a classification of binary increasing trees according to nodes types. Moreover, by the bijection between permutations, binary increasing trees and suitably defined path diagrams one can obtain continued fraction representations of the ordinary generating function of local types. The aim of this work is to introduce the notion of local types in $k$-Stirling permutations, to relate these local types with nodes types in $(k+1)$-ary increasing trees and to obtain a bijection with suitably defined path diagrams. Furthermore, we also present a path diagram representation of a related tree family called plane-oriented recursive trees, and the discuss the relation with ternary increasing trees.

Affiliated with

Also associated with

No associations

Rating

On Path diagrams and Stirling permutations 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 Path diagrams and Stirling permutations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Path diagrams and Stirling permutations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-64776