Cardinality of Rauzy classes

Vincent Delecroix[1]

  • [1] Institut de Mathématiques de Luminy (UMR 6206) Campus de Luminy, Case 907 13288 MARSEILLE Cedex 9

Annales de l’institut Fourier (2013)

  • Volume: 63, Issue: 5, page 1651-1715
  • ISSN: 0373-0956

Abstract

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Rauzy classes form a partition of the set of irreducible permutations. They were introduced as part of a renormalization algorithm for interval exchange transformations. We prove an explicit formula for the cardinality of each Rauzy class. Our proof uses a geometric interpretation of permutations and Rauzy classes in terms of translation surfaces and moduli spaces.

How to cite

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Delecroix, Vincent. "Cardinality of Rauzy classes." Annales de l’institut Fourier 63.5 (2013): 1651-1715. <http://eudml.org/doc/275583>.

@article{Delecroix2013,
abstract = {Rauzy classes form a partition of the set of irreducible permutations. They were introduced as part of a renormalization algorithm for interval exchange transformations. We prove an explicit formula for the cardinality of each Rauzy class. Our proof uses a geometric interpretation of permutations and Rauzy classes in terms of translation surfaces and moduli spaces.},
affiliation = {Institut de Mathématiques de Luminy (UMR 6206) Campus de Luminy, Case 907 13288 MARSEILLE Cedex 9},
author = {Delecroix, Vincent},
journal = {Annales de l’institut Fourier},
keywords = {Rauzy classes; Rauzy induction; interval exchange transformations; irreducible permutations; indecomposable permutations},
language = {eng},
number = {5},
pages = {1651-1715},
publisher = {Association des Annales de l’institut Fourier},
title = {Cardinality of Rauzy classes},
url = {http://eudml.org/doc/275583},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Delecroix, Vincent
TI - Cardinality of Rauzy classes
JO - Annales de l’institut Fourier
PY - 2013
PB - Association des Annales de l’institut Fourier
VL - 63
IS - 5
SP - 1651
EP - 1715
AB - Rauzy classes form a partition of the set of irreducible permutations. They were introduced as part of a renormalization algorithm for interval exchange transformations. We prove an explicit formula for the cardinality of each Rauzy class. Our proof uses a geometric interpretation of permutations and Rauzy classes in terms of translation surfaces and moduli spaces.
LA - eng
KW - Rauzy classes; Rauzy induction; interval exchange transformations; irreducible permutations; indecomposable permutations
UR - http://eudml.org/doc/275583
ER -

References

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