Interests:
My current interests are in two disparate areas: modern axiomatics of classical geometries especially Euclid's
Elements and integer partitions especially those realized as lattice points in
polyhedra. My first training is combinatorics, commutative algebra and combinatorial optimization.
Pre-prints and peer-reviewed publications:
Links to arxiv preprints may differ from final published versions. (* indicates undergraduate mentees)
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"On the equivalence of Playfair's axiom to the parallel postulate",
(with Brown, Castner*, Davis*, Seryozhenkov*, and Vargas*), Journal of Geometry, (2019) 110:42. 7 pages
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"Divisibility Tests Unified: Stacking the Trimmings for Sums",
Mathematics Magazine 92(2), (2019) 128-135.
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"Relaxed complete partitions: an error-correcting Bachet's problem",
(with Jorge Bruno), INTEGERS, 18, (2018) A41. 18 pages.
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"The Refined Lecture Hall Theorem via Abacus Diagrams",
(with Laura Bradford*, Meredith Harris*, Brant Jones, Alex Komarinski* and Carly Matson*),
The Ramanujan Journal 34, (2014) 163-176.
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"Bachet's problem: as few weights to weigh them all",
math/1010.5486. 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: