Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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POSETS ADMITTING THE LINEARITY OF ISOMETRIES

  • Hyun, Jong Youn (Institute of Mathematical Sciences Ewha Womans University) ;
  • Kim, Jeongjin (Department of Mathematics Myungji University) ;
  • Kim, Sang-Mok (Department of Mathematics Kwangwoon University)
  • Received : 2014.06.26
  • Published : 2015.05.31
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Abstract

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 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.

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References

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