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Rhizomes of ranked posets
Castro, Rachel H. Bingham, Aram
Castro, Rachel H.
Bingham, Aram
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2024-04
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Abstract
We introduce and study the notion of a rhizome for a ranked, partially ordered set (or poset) where each set of fixed rank is finite. A rhizome is defined as a minimal size subset of the elements of rank n such that each of the elements of rank n + 1 covers at least one element of the rhizome. Given a poset P with ranked parts Pn, we consider the function rP : N → N which gives the size of a rhizome for Pn, and study this function for examples like the Boolean lattice and Young's lattice.
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