Geodesic
On monotone permutations of $\ell$-cyclically ordered sets
Czechoslovak Mathematical Journal, Tome 56 (2006) no. 2, pp. 403-415 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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 
@article{CMJ_2006_56_2_a9,
     author = {Jakub{\'\i}k, J\'an},
     title = {On monotone permutations of $\ell$-cyclically ordered sets},
     journal = {Czechoslovak Mathematical Journal},
     pages = {403--415},
     year = {2006},
     volume = {56},
     number = {2},
     mrnumber = {2291745},
     zbl = {1164.06327},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2006_56_2_a9/}
}
TY  - JOUR
AU  - Jakubík, Ján
TI  - On monotone permutations of $\ell$-cyclically ordered sets
JO  - Czechoslovak Mathematical Journal
PY  - 2006
SP  - 403
EP  - 415
VL  - 56
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/CMJ_2006_56_2_a9/
LA  - en
ID  - CMJ_2006_56_2_a9
ER  - 
%0 Journal Article
%A Jakubík, Ján
%T On monotone permutations of $\ell$-cyclically ordered sets
%J Czechoslovak Mathematical Journal
%D 2006
%P 403-415
%V 56
%N 2
%U http://geodesic.mathdoc.fr/item/CMJ_2006_56_2_a9/
%G en
%F CMJ_2006_56_2_a9
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/