Flag vector pairs, fatness, and their bounds for 4-polytopes
DOI:
https://doi.org/10.11575/cdm.v16i3.71007Abstract
Recently Sjoberg and Ziegler showed a remarkable result that completely characterizes the flag vector pair (f0,f03) of any 4-dimensional polytopes. Motivated by their results and techniques, in this paper we show some necessary conditions for other remaining flag vector pairs such as (f0,f02), (f02,f03), (f1,f02), and (f1,f03) to be flag vector pairs of 4-dimensional convex polytopes. Results of this paper give some partial answers to the questions posed by Sj\" oberg and Ziegler. As an application of the bounds for flag vector pairs (f1,f03), in this paper we also provide some bounds of fatness function for certain 4-polytopes as well as 3-polytopes.
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