Contact information

Michael Slone mslone@ms.uky.edu
Digital Library Services
110 Margaret I. King Library
Lexington, KY 40506-0027
(859) 257-1218

Research interests

I study combinatorics, particularly aspects of combinatorics with connections to algebra and discrete geometry. Under the direction of Richard Ehrenborg, I wrote and defended a dissertation largely on the cd-index, an invariant which was originally defined as a way to encode the structure of a polytope as efficiently as possible. This compact representation has allowed the cd-index to act as a proxy for complicated geometric and poset-theoretical objects, simplifying many calculations. More recently I have become interested in combinatorial matrix theory and relations between graph theory and numerical analysis.

Publications

Affine and toric hyperplane arrangements, with Richard Ehrenborg and Margaret Readdy. Discrete Comput. Geom. (2009) 41:481—512. (arXiv)
A geometric approach to acyclic orientations, with Richard Ehrenborg. Order 26 (2009) 283—288 (arXiv)

In preparation

Mixing operators
Critical groups of cleft graphs

Talks

Get it online and keep it there: using Blacklight and CDL microservices to preserve and serve content. Part 2 of a joint presentation with Eric Weig and Richard Maiti to the UK campus-wide enterprise repository group. 1 April 2011.
Production infrastructure and data wrangling, with Eric Weig, 24 September 2008. Presentation at Meta-Morphosis: the University of Kentucky Film-to-Digital Institute.
Structure of toric arrangements, poset products, and cleft trees, 11 April, 2008. Doctoral defense.
What lies between structure and randomness, 5 December, 2007. Graduate Student Colloquium, University of Kentucky.
Restricted lattice paths and the cd-index of a product, 12 November, 2007. Combinatorics seminar, University of Kentucky.
How to use the cd-index, 30 October, 2007. Algebra and geometry seminar, University of Kentucky.
Nonintersecting lattice paths and the Jacobi-Trudi identity, 26 April, 2007. Seminar on representation theory of the symmetric group, University of Kentucky.
Generating functions and bases of the ring of symmetric functions, 19 April, 2007. Seminar on representation theory of the symmetric group, University of Kentucky.
Hall's marriage theorem, 14 February, 2007. Graduate Student Colloquium, University of Kentucky.
Older talks