Translated V-strict promotion order conjecture

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Let V={a,b,c}V=\{a,b,c\} be the three-element poset with a⋖ba\lessdot b and a⋖ca\lessdot c, let LV×[ℓ](Rq)\mathcal{L}_{V\times[\ell]}(R^q) denote the set of VV-strict labelings with restriction function RqR^q, and let Pro⁡\operatorname*{Pro} denote promotion. Translated V-strict promotion order conjecture. Promotion on LV×[ℓ](Rq)\mathcal{L}_{V\times[\ell]}(R^q) has order dividing

2q.2q.

This is presented as equivalent to the V-poset rowmotion conjecture; computational evidence and a reflection interpretation support it, but it remains unproved.

References

Primary source

Joseph Bernstein, Jessica Striker and Corey Vorland, “P-strict promotion and Q-partition rowmotion: the graded case”, arXiv:2205.04938 (2023).

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