论文标题

Jónsson和McKenzie从1982年开始的另一个问题:Posets连接力量的改进特性

Another Problem of Jónsson and McKenzie from 1982: Refinement Properties for Connected Powers of Posets

论文作者

Farley, Jonathan David

论文摘要

1982年,乔恩森(Jónsson)和麦肯齐(McKenzie)提出了以下问题:“在$ a^c \ cong b^d $ [$ a $ a $,$ b $,$ c $,$ b $,$ c $和$ d $ deppty posets和$ d $ deppty posets)中进行改进,并在“条件”下“条件” $ c $,$ c $,$ d $,$ d $和$ a^c $是有限的。也就是说,在这种情况下,是否有posets $ e $,$ x $,$ y $和$ z $,以便$ a \ a \ cong e^x $,$ b \ cong e^y $,$ c \ cong y \ times z $和$ d \ cong x \ cong x \ cong x \ times z $? 在此注释中,解决了此问题。

In 1982, Jónsson and McKenzie posed the following problem: "Find counter examples (or prove that none exist) to the refinement of $A^C\cong B^D$ [$A$, $B$, $C$, and $D$ non-empty posets] under" the condition "$C$, $D$, and $A^C$ are finite and connected." That is, in this situation, are there posets $E$, $X$, $Y$, and $Z$ such that $A\cong E^X$, $B\cong E^Y$, $C\cong Y\times Z$, and $D\cong X\times Z$? In this note, this problem is solved.

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