Interests:
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.
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"The Lecture Hall Theorem via Abacus Diagrams",
(with Laura Bradford, Meredith Harris, Brant Jones, Alex Komarinski and Carly Matson), math/1211.3702.
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"Relaxed r-complete partitions: an error-correcting Bachet's problem",
(with Jorge Bruno), math/1010.5485.
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"Bachet's problem: as few weights to weigh them all",
math/1010.5486.
Expository article. Revision in progress.
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"On the occurrence of large gaps in small contingency tables", math/0912.0702.
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"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.
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"Alternatives for Testing Total Dual Integrality",
(with András Sebő), Mathematical Programming, 132
(2012) 57 - 78. math/0803.2065.
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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.
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"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.
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"M-partitions: Optimal partitions of weight for one scale pan",
Discrete Mathematics , 289
(2004) 81 - 93. math.CO/0311230
Workshops given:
Dissertations: