arXiv subjects

Victor Reiner

Publications and source records attributed to Victor Reiner.

75 records · Page 5Linked to original sources

arXiv1997

On Subdivision Posets of Cyclic Polytopes

There are two related poset structures, the higher Stasheff-Tamari orders, on the set of all triangulations of the cyclic $d$ polytope with $n$ vertices. In this paper it is shown that both of them have the homotopy type of a sphere of dimension $n-d-3$. Moreover, we resolve positively a new special case of the \emph{Generalized Baues Problem}: The Baues poset of all polytopal decompositions of a cyclic polytope of dimension $d \leq 3$ has the homotopy type of a sphere of dimension $n-d-2$.

math.CO↗

arXiv1995

Not all free arrangements are $K(π,1)$

We produce a one-parameter family of hyperplane arrangements that are counterexamples to the conjecture of Saito that the complexified complement of a free arrangement is $K(π,1)$. These arrangements are the restriction of a one-parameter family of arrangements that arose in the study of tilings of certain centrally symmetric octagons. This other family is discussed as well.

math.AT↗

arXiv1994

The lattice of closure relations of a poset

In this paper we show that the set of closure relations on a finite poset P forms a supersolvable lattice, as suggested by Rota. Furthermore this lattice is dually isomorphic to the lattice of closed sets in a convex geometry (in the sense of Edelman and Jamison). We also characterize the modular elements of this lattice and compute its characteristic polynomial.

math.CO↗