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- W4327810412 abstract "Let $X$ be a finite set. A family $P$ of subsets of $X$ is called a convex geometry with ground set $X$ if (1) $emptyset, Xin P$; (2) $Acap Bin P$ whenever $A,Bin P$; and (3) if $Ain P$ and $Aneq X$, there is an element $alphain X-A$ such that $Acup{alpha}in P$. As a non-empty family of sets, a convex geometry has a well defined VC-dimension. In the literature, a second parameter, called convex dimension, has been defined expressly for these structures. Partially ordered by inclusion, a convex geometry is also a poset, and four additional dimension parameters have been defined for this larger class, called Dushnik-Miller dimension, Boolean dimension, local dimension, and fractional dimension, espectively. For each pair of these six dimension parameters, we investigate whether there is an infinite class of convex geometries on which one parameter is bounded and the other is not." @default.
- W4327810412 created "2023-03-19" @default.
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- W4327810412 date "2023-03-15" @default.
- W4327810412 modified "2023-09-29" @default.
- W4327810412 title "Concepts of Dimension for Convex Geometries" @default.
- W4327810412 doi "https://doi.org/10.48550/arxiv.2303.08945" @default.
- W4327810412 hasPublicationYear "2023" @default.
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