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arXiv · 2309.13535

Left absorption in products of countable orders

Garrett Ervin·Ethan Gu
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Abstract

We classify the countable linear orders $X$ for which there is an order $A$ with at least two points such that the lexicographic product $AX$ is isomorphic to $X$. Given such an $X$, we determine every corresponding order $A$, and identify when $X$ is isomorphic to its square. More generally, we characterize the countable orders that embed at least two disjoint convex copies of themselves.

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Garrett Ervin, Ethan Gu. 2023-09-24. Left absorption in products of countable orders. https://arxiv.org/abs/2309.13535

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