A relational structure is homomorphism-homogeneous if any homomorphism between its finite substructures extends to an endomorphism of the structure in question. In this note, we characterise all permutations on a finite set enjoying this property. To accomplish this, we switch from the more traditional view of a permutation as a set endowed with two linear orders to a different representation by a single linear order (considered as a directed graph with loops) whose non-loop edges are coloured in two colours, thereby `splitting' the linear order into two posets.
@article{10_37236_2271,
author = {Igor Dolinka and \'Eva Jung\'abel},
title = {Finite homomorphism-homogeneous permutations via edge colourings of chains},
journal = {The electronic journal of combinatorics},
year = {2012},
volume = {19},
number = {4},
doi = {10.37236/2271},
zbl = {1267.05007},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2271/}
}
TY - JOUR
AU - Igor Dolinka
AU - Éva Jungábel
TI - Finite homomorphism-homogeneous permutations via edge colourings of chains
JO - The electronic journal of combinatorics
PY - 2012
VL - 19
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/2271/
DO - 10.37236/2271
ID - 10_37236_2271
ER -
%0 Journal Article
%A Igor Dolinka
%A Éva Jungábel
%T Finite homomorphism-homogeneous permutations via edge colourings of chains
%J The electronic journal of combinatorics
%D 2012
%V 19
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/2271/
%R 10.37236/2271
%F 10_37236_2271
Igor Dolinka; Éva Jungábel. Finite homomorphism-homogeneous permutations via edge colourings of chains. The electronic journal of combinatorics, Tome 19 (2012) no. 4. doi: 10.37236/2271
