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Shelling and triangulating the (extra)ordinary polytope
Margaret M. Bayer
Ordinary polytopes were introduced by Bisztriczky as a (nonsimplicial) generalization of cyclic polytopes. We show that the colex order of facets of the ordinary polytope is a shel…
Flag vectors of multiplicial polytopes
Margaret M. Bayer
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 vecto…
A combinatorial study of multiplexes and ordinary polytopes
Margaret M. Bayer, Aaron M. Bruening, Joshua Stewart
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 comb…
Generalizations of Eulerian partially ordered sets, flag numbers, and the Mobius function
Margaret M. Bayer, Gabor Hetyei
A partially ordered set is r-thick if every nonempty open interval contains at least r elements. This paper studies the flag vectors of graded, r-thick posets and shows the smalles…
Signs in the cd-index of Eulerian partially ordered sets
Margaret M. Bayer
A graded partially ordered set is Eulerian if every interval has the same number of elements of even rank and of odd rank. Face lattices of convex polytopes are Eulerian. For Euler…
Flag vectors of Eulerian partially ordered sets
Margaret M. Bayer, Gabor Hetyei
The closed cone of flag vectors of Eulerian partially ordered sets is studied. It is completely determined up through rank seven. Half-Eulerian posets are defined. Certain limit po…