Matrices of 3iet preserving morphisms

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dc.creatorAmbroz, P.
dc.creatorMasáková, Z.
dc.creatorPelantová, E.
dc.date2007-02-12
dc.date.accessioned2026-07-07T07:46:22Z
dc.date.available2026-07-07T07:46:22Z
dc.descriptionWe study matrices of morphisms preserving the family of words coding 3-interval exchange transformations. It is well known that matrices of morphisms preserving sturmian words (i.e. words coding 2-interval exchange transformations with the maximal possible factor complexity) form the monoid $\{\boldsymbol{M}\in\mathbb{N}^{2\times 2} | \det\boldsymbol{M}=\pm1\} = \{\boldsymbol{M}\in\mathbb{N}^{2\times 2} | \boldsymbol{M}\boldsymbol{E}\boldsymbol{M}^T = \pm\boldsymbol{E}\}$, where $\boldsymbol{E} = (\begin{smallmatrix}0&1 -1&0\end{smallmatrix})$. We prove that in case of exchange of three intervals, the matrices preserving words coding these transformations and having the maximal possible subword complexity belong to the monoid $\{\boldsymbol{M}\in\mathbb{N}^{3\times 3} | \boldsymbol{M}\boldsymbol{E}\boldsymbol{M}^T = \pm\boldsymbol{E},\ \det\boldsymbol{M}=\pm 1\}$, where $\boldsymbol{E} = \Big(\begin{smallmatrix}0&1&1 -1&0&1 -1&-1&0\end{smallmatrix}\Big)$.
dc.description26 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/math/0702336
dc.identifierhttp://arxiv.org/abs/math/0702336
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/123804
dc.subjectCombinatorics
dc.subject68R15; 15A36
dc.titleMatrices of 3iet preserving morphisms
dc.typetext

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