Exchanges of the intervals and minimal sequences. (Echanges de trois intervalles et suites minimales.) (French) Zbl 0902.68153

Summary: This work is a study of minimal sequences generated by exchanges of three intervals. We employ the notion of “word graph”. The main result is that the evolution of “\(n\)-segements” is completely defined by 62 substitutions acting on alphabets of 3 or 4 letters.


68R15 Combinatorics on words


word graph
Full Text: DOI


[1] Arnoux, P.; Rauzy, G., Représentation géométrique des suites de complexité 2n + 1, Bull. soc. math. France, 119, 199-215, (1991) · Zbl 0789.28011
[2] Keane, M.S., Interval exchanges transformations, Math. Z., 141, 5, 25-31, (1975) · Zbl 0278.28010
[3] Keane, A.; Rauzy, G., Stricte ergodicité des échanges d’intervalles, Math. Z., 174, 203-212, (1980) · Zbl 0479.28012
[4] Rauzy, G., Echanges d’intervalles et transformations induites, Acta arithmetica, XXXIV, 315-328, (1979) · Zbl 0414.28018
[5] Santini, M.L., Echanges de trois intervalles, Thèse de l’université d’aix-Marseille II, (1994)
[6] Veech, W.A., Topological dynamics, Bull. amer. math. soc., 83, 5, 775-830, (1977) · Zbl 0384.28018
[7] Veech, W.A., Interval exchange transformations, J. d’analyse, 33, 222-272, (1978) · Zbl 0455.28006
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.