1,451 research outputs found
Higher Bruhat orders of types B and C
We propose versions of higher Bruhat orders for types and . This is
based on a theory of higher Bruhat orders of type~A and their geometric
interpretations (due to Manin--Shekhtman, Voevodskii--Kapranov, and Ziegler),
and on our study of the so-called symmetric cubillages of cyclic zonotopes.Comment: 22 pages, 12 figures, a reference is added, a misprint in commutative
diagram is correcte
A Suspension Lemma for Bounded Posets
Let and be bounded posets. In this note, a lemma is introduced that
provides a set of sufficient conditions for the proper part of being
homotopy equivalent to the suspension of the proper part of~. An application
of this lemma is a unified proof of the sphericity of the higher Bruhat orders
under both inclusion order (a known proved earlier by Ziegler) and single step
inclusion order (which was not previously known)
Condorcet domains of tiling type
A Condorcet domain (CD) is a collection of linear orders on a set of
candidates satisfying the following property: for any choice of preferences of
voters from this collection, a simple majority rule does not yield cycles. We
propose a method of constructing "large" CDs by use of rhombus tiling diagrams
and explain that this method unifies several constructions of CDs known
earlier. Finally, we show that three conjectures on the maximal sizes of those
CDs are, in fact, equivalent and provide a counterexample to them.Comment: 16 pages. To appear in Discrete Applied Mathematic
- …