1Department of MathematicsRyerson University350 Victoria St.Toronto, ON, Canada, M5B 2K3 2University of CalgaryDepartment of Mathematics and StatisticsCalgary, Alberta, Canada T2N 1N4
The electronic journal of combinatorics, Tome 29 (2022) no. 3
The distinguishing number of a structure is the smallest size of a partition of its elements so that only the trivial automorphism of the structure preserves the partition. We show that for any countable subset of the positive real numbers, the corresponding countable Urysohn metric space, when it exists, has distinguishing number two or is infinite. While it is known that a sufficiently large finite primitive structure has distinguishing number two, unless its automorphism group is not the full symmetric group or alternating group, the infinite case is open and these countable Urysohn metric spaces provide further confirmation toward the conjecture that all primitive homogeneous countably infinite structures have distinguishing number two or else is infinite.
A. Bonato
1
;
C. Laflamme
2
;
M. Pawliuk
2
;
N. Sauer
2
1
Department of MathematicsRyerson University350 Victoria St.Toronto, ON, Canada, M5B 2K3
2
University of CalgaryDepartment of Mathematics and StatisticsCalgary, Alberta, Canada T2N 1N4
@article{10_37236_8370,
author = {A. Bonato and C. Laflamme and M. Pawliuk and N. Sauer},
title = {Distinguishing number of universal homogeneous {Urysohn} metric spaces},
journal = {The electronic journal of combinatorics},
year = {2022},
volume = {29},
number = {3},
doi = {10.37236/8370},
zbl = {1529.54011},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8370/}
}
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AU - C. Laflamme
AU - M. Pawliuk
AU - N. Sauer
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A. Bonato; C. Laflamme; M. Pawliuk; N. Sauer. Distinguishing number of universal homogeneous Urysohn metric spaces. The electronic journal of combinatorics, Tome 29 (2022) no. 3. doi: 10.37236/8370
