Bull. Korean Math. Soc. 2015; 52(3): 999-1006
Printed May 31, 2015
https://doi.org/10.4134/BKMS.2015.52.3.999
Copyright © The Korean Mathematical Society.
Jong Youn Hyun, Jeongjin Kim, and Sang-Mok Kim
Ewha Womans University, Myungji University, Kwangwoon University
In this paper, we deal with a characterization of the posets with the property that every poset isometry of $\mathbb{F}^n_q$ fixing the origin is a linear map. We say such a poset to be {\it admitting the linearity of isometries}. We show that a poset $P$ admits the linearity of isometries over $\mathbb{F}^n_q$ if and only if $P$ is a disjoint sum of chains of cardinality $2$ or $1$ when $q=2$, or $P$ is an anti-chain otherwise.
Keywords: $P$-isometries, $P$-isometry group, poset metric
MSC numbers: 94B05
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