Document Type
Article
Publication Title
Journal of Discrete Mathematics
Publication Date
2013
Page Number
1820
Keywords
simplicial complexes, threshold complex, qualitative probability orders
Disciplines
Law | Other Mathematics | Probability
Abstract
The goal of this paper is to introduce a new class of simplicial complexes that naturally generalize the threshold complexes. These will be derived from qualitative probability orders on subsets of a finite set that generalize subset orders induced by probability measures. We show that this new class strictly contains the threshold complexes and is strictly contained in the shifted complexes. We conjecture that this class of complexes is exactly the set of strongly acyclic complexes, a class that has previously appeared in the context of cooperative games. Beyond the results themselves, this new class of complexes allows us to refine our understanding of one-point extensions of a particular oriented matroid.
Recommended Citation
Paul H. Edelman, Tatiana Gvozdeva, and Arkadii Slinko,
Simplicial Complexes Obtained from Qualitative Probability Orders, 27 Journal of Discrete Mathematics. 1820
(2013)
Available at: https://scholarship.law.vanderbilt.edu/faculty-publications/650