Geodesic
On monotone permutations of $\ell$-cyclically ordered sets
Czechoslovak Mathematical Journal, Tome 56 (2006) no. 2, pp. 403-415.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

For an $\ell $-cyclically ordered set $M$ with the $\ell $-cyclic order $C$ let $P(M)$ be the set of all monotone permutations on $M$. We define a ternary relation $\overline{C}$ on the set $P(M)$. Further, we define in a natural way a group operation (denoted by $\cdot $) on $P(M)$. We prove that if the $\ell $-cyclic order $C$ is complete and $\overline{C}\ne \emptyset $, then $(P(M), \cdot ,\overline{C})$ is a half cyclically ordered group.
Classification : 06F15
Keywords: $\ell $-cyclically ordered set; completeness; monotone permutation; half cyclically ordered group 
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     author = {Jakub{\'\i}k, J\'an},
     title = {On monotone permutations of $\ell$-cyclically ordered sets},
     journal = {Czechoslovak Mathematical Journal},
     pages = {403--415},
     publisher = {mathdoc},
     volume = {56},
     number = {2},
     year = {2006},
     mrnumber = {2291745},
     zbl = {1164.06327},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2006__56_2_a9/}
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Jakubík, Ján. On monotone permutations of $\ell$-cyclically ordered sets. Czechoslovak Mathematical Journal, Tome 56 (2006) no. 2, pp. 403-415. http://geodesic.mathdoc.fr/item/CMJ_2006__56_2_a9/