M
Michael Slone
Researcher at University of Kentucky
Publications - 8
Citations - 76
Michael Slone is an academic researcher from University of Kentucky. The author has contributed to research in topics: Partially ordered set & Hyperplane. The author has an hindex of 4, co-authored 8 publications receiving 75 citations.
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Affine and Toric Hyperplane Arrangements
TL;DR: The Billera–Ehrenborg–Readdy map between the intersection lattice and face lattice of a central hyperplane arrangement is extended to affine and toric hyperplane arrangements and Zaslavsky’s fundamental results on the number of regions are generalized.
Journal ArticleDOI
Affine and toric hyperplane arrangements
TL;DR: In this paper, the authors extend the Billera-Ehrenborg-Readdy map between the intersection lattice and face lattice of a central hyperplane arrangement to affine and toric hyperplane arrangements.
Posted Content
Homological combinatorics and extensions of the cd-index
TL;DR: In this article, coalgebras are used to compute invariants of toric and affine arrangements as well as of poset products, and for acyclic orientations and critical groups of graphs.
Journal ArticleDOI
Affine and toric arrangements
TL;DR: In this paper, the authors extend the Billera map between the intersection lattice and face lattice of a central hyperplane arrangement to affine and toric hyperplane arrangements, and generalize Zaslavsky's fundamental results on the number of regions.
Journal ArticleDOI
A Geometric Approach to Acyclic Orientations
Richard Ehrenborg,Michael Slone +1 more
TL;DR: The set of acyclic orientations of a connected graph with a given sink has a natural poset structure and is the disjoint union of distributive lattices, which is a geometric proof of a result of Jim Propp.