MathDBRegularity of finitary semi-upho posets
Regularity of finitary semi-upho posets
A semi-upho poset is a poset satisfying the corresponding principal-filter self-similarity condition for semi-upho posets; it is finitary when its relevant rank layers are finite. A semi-upho poset is regular if it lies in the image of the forgetful map from finitary colored semi-upho posets.
Regularity conjecture. Every finitary semi-upho poset is regular.
This is the semi-upho counterpart of the monoid-representation problem for upho posets. The source states that even the finite-type graded cases remain open.
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Sources & referencesView supporting material
Primary source
Ziyao Fu, Yulin Peng and Yuchong Zhang, “The monoid representation of upho posets and total positivity”, arXiv:2411.04123 (2024).
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