Relationships Among Flag <Emphasis Type="Italic">f</Emphasis>-Vector Inequalities for Polytopes |
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Authors: | Email author" target="_blank">Catherine?StensonEmail author |
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Institution: | (1) Department of Mathematics, Juniata College, Huntingdon, PA 16652, USA |
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Abstract: | We examine linear inequalities satisfied by the
flag $f$-vectors of polytopes. One source of these inequalities
is the toric $g$-vector; convolutions of its entries are non-negative
for rational polytopes. We prove a conjecture of Meisinger about a
redundancy in these inequalities. Another source of inequalities is
the {\bf cd}-index; among all $d$-polytopes, each {\bf cd}-index coefficient
is minimized on the $d$-simplex. We show that not all of the {\bf cd}-index
inequalities are implied by the toric $g$-vector inequalities, and that not all of the toric $g$-vector inequalities are implied by the {\bf cd}-index
inequalities.
Finally, we show that some inequalities from
convolutions of {\bf cd}-index coefficients are implied by other
{\bf cd}-index inequalities. |
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Keywords: | |
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