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arXiv · 2112.06843

Toric Promotion

Colin Defant
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Abstract

We introduce toric promotion as a cyclic analogue of Schützenberger's promotion operator. Toric promotion acts on the set of labelings of a graph $G$. We discuss connections between toric promotion and previously-studied notions such as toric posets and friends-and-strangers graphs. Our main theorem provides a surprisingly simple description of the orbit structure of toric promotion when $G$ is a forest.

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Colin Defant. 2022-09-18. Toric Promotion. https://arxiv.org/abs/2112.06843

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