How rigid the finite ultrametric spaces can be?

O. Dovgoshey; E. Petrov; H. M. Teichert

doi:10.1007/s11784-016-0329-5

How rigid the finite ultrametric spaces can be?

O. Dovgoshey, E. Petrov^*, H. M. Teichert

^*Corresponding author for this work

Institute of Mathematics

Ukrainian National Academy of Sciences

23 Citations (Scopus)

Abstract

A metric space X is rigid if the isometry group of X is trivial. The finite ultrametric spaces X with |X| ≥ 2 are not rigid since for every such X there is a self-isometry having exactly |X|−2 fixed points. Using the representing trees we characterize the finite ultrametric spaces X for which every self-isometry has at least |X|−2 fixed points. Some other extremal properties of such spaces and related graph theoretical characterizations are also obtained.

Original language	English
Journal	Journal of Fixed Point Theory and Applications
Volume	19
Issue number	2
Pages (from-to)	1083-1102
Number of pages	20
ISSN	1661-7738
DOIs	https://doi.org/10.1007/s11784-016-0329-5
Publication status	Published - 01.06.2017

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10.1007/s11784-016-0329-5

Cite this

@article{32c8799653c842d6a153cc5de62ac5bc,

title = "How rigid the finite ultrametric spaces can be?",

abstract = "A metric space X is rigid if the isometry group of X is trivial. The finite ultrametric spaces X with |X| ≥ 2 are not rigid since for every such X there is a self-isometry having exactly |X|−2 fixed points. Using the representing trees we characterize the finite ultrametric spaces X for which every self-isometry has at least |X|−2 fixed points. Some other extremal properties of such spaces and related graph theoretical characterizations are also obtained.",

author = "O. Dovgoshey and E. Petrov and Teichert, \{H. M.\}",

year = "2017",

month = jun,

day = "1",

doi = "10.1007/s11784-016-0329-5",

language = "English",

volume = "19",

pages = "1083--1102",

journal = "Journal of Fixed Point Theory and Applications",

issn = "1661-7738",