arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2005.03255math.CO
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1978年,《秩序》杂志的一位未来主编提出了一个问题:有限连通偏序集的自同态偏序集是否告诉我们偏序集是连通的?

An Issue Raised in 1978 by a Then-Future Editor-in-Chief of the Journal "Order": Does the Endomorphism Poset of a Finite Connected Poset Tell Us That the Poset Is Connected?

Jonathan David Farley

摘要:

在1978年,Dwight Duffus--2010年至2018年《秩序》杂志的主编和1991年至2005年埃默里大学数学系的主席--写道:“$P$是连通的并不明显,$P^P$同构于$Q^Q$意味着$Q$是连通的”,其中$P$和$Q$是有限的非空偏序集。我们表明,事实上,在这些假设下$Q$连接和$P\cong Q$。

英文摘要:

In 1978, Dwight Duffus---editor-in-chief of the journal "Order" from 2010 to 2018 and chair of the Mathematics Department at Emory University from 1991 to 2005---wrote that "it is not obvious that $P$ is connected and $P^P$ isomorphic to $Q^Q$ implies that $Q$ is connected," where $P$ and $Q$ are finite non-empty posets. We show that, indeed, under these hypotheses $Q$ is connected and $P\cong Q$.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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