My primary research foci are in combinatorics and computational algebra.
The questions and problems I think about often have a geometric flavour but not always.
They usually involve some combination of:
Gröbner bases, Toric ideals, Hilbert bases, Total Dual Integrality, Lattice Point Enumeration,
Integer Partitions. I reserve the right to add more interests to this short list.
Pre-prints and peer-reviewed publications:
The links below may differ ever so slightly from final published versions.
"The Lecture Hall Theorem via Abacus Diagrams",
(with Laura Bradford, Meredith Harris, Brant Jones, Alex Komarinski and Carly Matson), math/1211.3702.
"Relaxed r-complete partitions: an error-correcting Bachet's problem",
(with Jorge Bruno), math/1010.5485.
"Bachet's problem: as few weights to weigh them all",
Expository article. Revision in progress.
"On the occurrence of large gaps in small contingency tables", math/0912.0702.
"Ehrhart clutters: regularity and max-flow min-cut",
(with José Martínez-Bernal and Rafael H. Villarreal),
Elec. J. Combinatorics, 17, (2010), R52. math/0902.1354.
"Alternatives for Testing Total Dual Integrality",
(with András Sebő), Mathematical Programming, 132
(2012) 57 - 78. math/0803.2065.
An earlier, restricted version of "Alternatives for Testing Total Dual Integrality" appeared in
12th International IPCO Conference, Ithaca, NY, USA, June 25-27, 2007, Proceedings
Springer Lecture Notes in Computer Science, 4513 (2007) 382 - 396.
"Toric initial ideals of $\Delta$-normal configurations:
Cohen-Macaulayness and degree bounds", (with Rekha Thomas),
Journal of Algebraic Combinatorics , 21
(2005) 247 - 268. math.AC/0308109.
"M-partitions: Optimal partitions of weight for one scale pan",
Discrete Mathematics , 289
(2004) 81 - 93. math.CO/0311230