Some families of ideal-homogeneous posets
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A partially ordered set $P$ is \textit{ideal-homogeneous} provided that for any ideals $I$ and $J$, if $ I\cong_{\sigma}J$, then there exists an automorphism $\sigma^*$ such that $\sigma^*|_I = \sigma$. Behrendt~\cite{Beh} characterizes the ideal-homogeneous partially ordered sets of height $1$. In this paper, we characterize the ideal-homogeneous partially ordered sets of height 2 and find some families of ideal-homogeneous partially ordered sets.
Abstract
A partially ordered set $P$ is \textit{ideal-homogeneous} provided that for any ideals $I$ and $J$, if $ I\cong_{\sigma}J$, then there exists an automorphism $\sigma^*$ such that $\sigma^*|_I = \sigma$. Behrendt~\cite{Beh} characterizes the ideal-homogeneous partially ordered sets of height $1$. In this paper, we characterize the ideal-homogeneous partially ordered sets of height 2 and find some families of ideal-homogeneous partially ordered sets.
참고문헌 (2)
- G. Behrendt, "Homogeneity in Finite Ordered Sets", Order, 10(1), pp.65~75 (1993)
- B. A. Davey, "Introduction to Lattices and Order" (2002), Cambridge University Press