Posets Admitting the Linearity of Isometries

Abstract

Abstract. In this paper, we deal with a characterization of the posets with the property that every poset isometry of 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 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.