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.
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机译：在本文中，我们处理具有特征的样态的特征，即固定原点的$ mathbb {F} ^ n_q $的每个样态等轴测图都是线性图。我们说这样的姿态是{它承认等轴线的线性}。我们证明，当且仅当$ P $是基数$ 2 $或$ 1 $（当$ q = 2 $时）不相交的总和时，状态子$ P $才接受$ mathbb {F} ^ n_q $上的等线性线性。否则$ P $是反链。
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