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

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