Posets admitting the linearity of isometries

Abstract

In this paper, we deal with a characterization of the posets with the property that every poset isometry of 𝔽n q fixing the origin is a linear map. We say such a poset to be admitting the linearity of isome-tries. We show that a poset P admits the linearity of isometries over 𝔽n qif 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. ©2015 Korean Mathematical Society.