## Lapointe, Mélodie - Number of orbits of Discrete Interval Exchanges

dmtcs:4951 - Discrete Mathematics & Theoretical Computer Science, May 16, 2019, Vol. 21 no. 3 - https://doi.org/10.23638/DMTCS-21-3-17
Number of orbits of Discrete Interval Exchanges

Authors: Lapointe, Mélodie

A new recursive function on discrete interval exchange transformation associated to a composition of length $r$, and the permutation $\sigma(i) = r -i +1$ is defined. Acting on composition $c$, this recursive function counts the number of orbits of the discrete interval exchange transformation associated to the composition $c$. Moreover, minimal discrete interval exchanges transformation i.e. the ones having only one orbit, are reduced to the composition which label the root of the Raney tree. Therefore, we describe a generalization of the Raney tree using our recursive function.

Volume: Vol. 21 no. 3
Section: Combinatorics
Published on: May 16, 2019
Submitted on: November 1, 2018
Keywords: Mathematics - Combinatorics

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