Geodesic
Number of orbits of Discrete Interval Exchanges
Discrete mathematics & theoretical computer science, Tome 21 (2019) no. 3.

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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.
DOI : 10.23638/DMTCS-21-3-17
Classification : 05C05 
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     author = {Lapointe, M\'elodie},
     title = {Number of orbits of {Discrete} {Interval} {Exchanges}},
     journal = {Discrete mathematics & theoretical computer science},
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Lapointe, Mélodie. Number of orbits of Discrete Interval Exchanges. Discrete mathematics & theoretical computer science, Tome 21 (2019) no. 3. doi : 10.23638/DMTCS-21-3-17. http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-21-3-17/

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