1. On monotone permutations of $\ell$-cyclically ordered sets
- Creator:
- Jakubík, Ján
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- $\ell $-cyclically ordered set;, completeness, monotone permutation, and half cyclically ordered group
- Language:
- English
- Description:
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public