| Title:
|
On monotone permutations of $\ell$-cyclically ordered sets (English) |
| Author:
|
Jakubík, Ján |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
2 |
| Year:
|
2006 |
| Pages:
|
403-415 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
$\ell $-cyclically ordered set |
| Keyword:
|
completeness |
| Keyword:
|
monotone permutation |
| Keyword:
|
half cyclically ordered group |
| MSC:
|
06F15 |
| idZBL:
|
Zbl 1164.06327 |
| idMR:
|
MR2291745 |
| . |
| Date available:
|
2009-09-24T11:34:10Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128075 |
| . |
| Reference:
|
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| Reference:
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| . |
