论文标题

1978年由当时的“订单”总编辑提出的问题:有限连接的Poset的内态POSET告诉我们,Poset是连接的吗?

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?

论文作者

Farley, Jonathan David

论文摘要

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.我们表明,实际上,根据这些假设$ Q $连接,$ p \ cong Q $。

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 $P\cong Q$.

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