Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Flag vectors of multiplicial polytopes   Bisztriczky introduced the multiplex as a generalization of the simplex. A
polytope is multiplicial if all its faces are multiplexes. In this paper it is
proved that the flag vectors of multiplicial polytopes depend only on their
face vectors. A special class of multiplicial polytopes, also discovered by
Bisztriczky, is comprised of the ordinary polytopes. These are a natural
generalization of the cyclic polytopes. The flag vectors of ordinary polytopes
are determined. This is used to give a surprisingly simple formula for the
h-vector of the ordinary d-polytope with n+1 vertices and characteristic k:
h_i=binom{k-d+i}{i}+(n-k)binom{k-d+i-1}{i-1}, for i at most d/2. In addition, a
construction is given for 4-dimensional multiplicial polytopes having
two-thirds of their vertices on a single facet, answering a question of
Bisztriczky.

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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: cs
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin