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A Combinatorial Study of Multiplexes and Ordinary Polytopes

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Abstract

Bisztriczky defines a multiplex as a generalization of a simplex, and an ordinary polytope as a generalization of a cyclic polytope. This paper presents results concerning the combinatorics of multiplexes and ordinary polytopes. The flag vector of the multiplex is computed, and shown to equal the flag vector of a many-folded pyramid over a polygon. Multiplexes, but not other ordinary polytopes, are shown to be elementary. It is shown that all complete subgraphs of the graph of a multiplex determine faces of the multiplex. The toric h -vectors of the ordinary five-dimensional polytopes are given. Graphs of ordinary polytopes are studied. Their chromatic numbers and diameters are computed, and they are shown to be Hamiltonian.

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Received December 8, 2000, and in revised form June 21, 2001. Online publication November 2, 2001.

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Bayer, M., Bruening, A. & Stewart, J. A Combinatorial Study of Multiplexes and Ordinary Polytopes. Discrete Comput Geom 27, 49–63 (2002). https://doi.org/10.1007/s00454-001-0051-x

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