On monotone permutations of ℓ -cyclically ordered sets

Ján Jakubík

Czechoslovak Mathematical Journal (2006)

  • Volume: 56, Issue: 2, page 403-415
  • ISSN: 0011-4642

Abstract

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For an ℓ -cyclically ordered set M with the ℓ -cyclic order C let P ( M ) be the set of all monotone permutations on M . We define a ternary relation C ¯ on the set P ( M ) . Further, we define in a natural way a group operation (denoted by · ) on P ( M ) . We prove that if the ℓ -cyclic order C is complete and C ¯ ≠ ∅ , then ( P ( M ) , · , C ¯ ) is a half cyclically ordered group.

How to cite

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Jakubík, Ján. "On monotone permutations of $\ell $-cyclically ordered sets." Czechoslovak Mathematical Journal 56.2 (2006): 403-415. <http://eudml.org/doc/31037>.

@article{Jakubík2006,
abstract = {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.},
author = {Jakubík, Ján},
journal = {Czechoslovak Mathematical Journal},
keywords = {$\ell $-cyclically ordered set; completeness; monotone permutation; half cyclically ordered group; completeness; monotone permutation; half cyclically ordered group},
language = {eng},
number = {2},
pages = {403-415},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On monotone permutations of $\ell $-cyclically ordered sets},
url = {http://eudml.org/doc/31037},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Jakubík, Ján
TI - On monotone permutations of $\ell $-cyclically ordered sets
JO - Czechoslovak Mathematical Journal
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 2
SP - 403
EP - 415
AB - 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.
LA - eng
KW - $\ell $-cyclically ordered set; completeness; monotone permutation; half cyclically ordered group; completeness; monotone permutation; half cyclically ordered group
UR - http://eudml.org/doc/31037
ER -

References

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