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Bull. Korean Math. Soc. 2016; 53(4): 971-983
Printed July 31, 2016
https://doi.org/10.4134/BKMS.b150204
Copyright © The Korean Mathematical Society.
Some families of ideal-homogeneous posets
Gab-Byung Chae, Minseok Cheong, and Sang-Mok Kim
Wonkwang University, Korea University, Kwangwoon University
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.
Keywords: poset, finite ordered set, homogeneity
MSC numbers: 06A06, 20B25
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