2
$\begingroup$

In his unpublished article, Combinatorial properties of triangulations of oriented matroids, Julian Webster proves that every triangulation of an oriented matroid is partitionable.

Does this result appear somewhere in the published literature? If so, where?

Edits:

  1. Webster himself does not know if this result has been published elsewhere.

  2. Two excellent resources for triangulations of oriented matroids are Triangulations: Structures for Algorithms and Applications in the realizable case and Triangulations of Oriented Matroids in the general case. Neither of these sources discuss partitions of triangulations of oriented matroids.

  3. A simplicial complex $\Delta$ is partitionable if there is a function $\phi : F \to \Delta$ on the facets of $\Delta$ such that the set of intervals $\{[\phi(f), f]~|~f \in F\} $ is a partition of the faces of $\Delta$.
Improve this question
$\endgroup$
3
  • $\begingroup$ Can you please define what do you mean by partitionable? $\endgroup$
    – Anubhav Mukherjee
    Commented Sep 28, 2017 at 11:54
  • $\begingroup$ Partitionable means "partitionable as an abstract simplicial complex on the set of all one-simplices in the triangulation". For the definition of partitionable simplicial complex see Definition 2.5 in this article: arxiv.org/abs/1504.04279. $\endgroup$
    – Aaron Dall
    Commented Sep 28, 2017 at 12:02
  • 1
    $\begingroup$ Since I am an author of the two "excellent sources" I should give my opinion: no, as far as I know this is not published. When I was writing the "Triangulations of Oriented Matroids" paper I thought about this and the way I recall it (this was 20 years ago) is that at some point I thought I had a proof but then was not convinced by it and left the question out of the paper. $\endgroup$
    – Francisco Santos
    Commented Oct 17, 2017 at 1:22

0

Reset to default

You must log in to answer this question.