Research

Refereed Publications

• Group Actions and Messiaen's Modes of Limited Transposition, under review.
  
  
• (with Jacob Charboneau and Stephen Gagola III) Strong complete mappings for 2-groups. Discrete Math. 348 (2025), no. 10, Paper No. 114568. pdf.
  
  
• (with Stephen Gagola III) Strong complete mappings for 3-groups. Discrete Math. 345 (2022), no. 1, Paper No. 112643. pdf.
  
  
• Linear Operator Identities in Quasigroups. Comment. Math. Univ. Carolinae 63 (2022), no.1, 1-9. pdf.
  
  
• (with Roy Joshua) Explicit Chow-Lefschetz decompositions of Kummer manifolds. K-theory: Proceedings of the International Colloquium, Mumbai, 2016 (2018), 155-194. pdf.
  
  
• Symmetric Linear Operator Identities in Quasigroups. Comment. Math. Univ. Carolinae 58 (2017), no.4, 401-417. pdf.
  
  
• On Generalized Associativity in Groupoids. Quasigroups and Related Systems 24 (2016), no. 1, 1-6. pdf
  
  
• (with Lucas Lee) Connectivity of the zero-divisor graph for finite rings. Involve 9 (2016), no. 3, 415-422. pdf
  
  
• (with B. Burns, H. Dohrmann, H. Hoganson, O. Sobieska, and Z. Woods) Splitting techniques and Betti numbers of secant powers. Involve 9 (2016), no. 5, 737-750. pdf
  
  
• (with Max Forlini) The Linear Chromatic Number of a Sperner Family, Discrete Applied Mathematics 171 (2014), 1-8. pdf
  
  
• The Representation Number of Some Sparse Graphs, Discrete Mathematics 312 (2012), no. 22, 3417-3423. pdf
  
  
• (with A. Arp, M. Kaminski, D. Vernon, J. VanExel, and C. Washington) The varieties of Bol-Moufang quasigroups defined by a single operation, Quasigroups and Related Systems 20 (2012), 1-10. pdf
  
  
• (with Tony Evans and Dan Pritikin) Representation Numbers of Complete Multipartite Graphs, Discrete Mathematics 312 (2012), no. 6, 1158-1165. pdf
  
  
• (with Roy Joshua) Toric Residue Codes: I. Finite Fields and Their Applications 17, no. 1 (2011), 15-50. pdf
  
  
• (with Paul Larson) Small-sum pairs in abelian groups. J. de Th. de Nombres de Bordeaux 22, no. 3 (2010), 525-535. pdf
  
  
• (with Tony Evans and Dan Pritikin) Representation Numbers of Stars. Integers 10 (2010), 733-745. pdf
  
  
• (with M. Boggess, T. Jackson-Henderson, I. Jimenez, R. Karpman, A. Kinzel, D. Pritikin) On the unitary Cayley graph of a finite ring.
  Electronic Journal of Combinatorics 16 (2009), no. 1, Research Paper 117, 13 pp. pdf. Erratum.
  
  
• (with Roy Joshua) Lefschetz Decompositions for Quotient Varieties.
  Journal of K-theory 3 (2009), no. 3, 547-560. pdf
  
  
• (with Tao Jiang and Zevi Miller) Asymptotic determination of edge-bandwidth of multidimensional grids and Hamming graphs.
  SIAM Journal on Discrete Mathematics 22 (2008), no. 2, 425-449. pdf
  
  
• (with Tao Jiang and Dan Pritikin) Edge-bandwidth of the triangular grid.
  Electronic Journal of Combinatorics 14 (2007), no. 1, Research Paper 67, 11 pp. pdf
  
  
• A mod-l vanishing theorem of Beilinson-Soule type.
  Journal of Pure and Applied Algebra 208 (2007), no. 2, 555-560. pdf
  
  
• (with Lucas Lee) Homology of zero-divisors.
  Rocky Mountain Journal of Mathematics 37 (2007), no. 4, 1105-1126. pdf. Erratum.
  
  
• (with Roy Joshua) Kunneth decompositions for quotient varieties.
  Indagationes Mathematicae 17 (2006), no. 3, 319-344. pdf
  
  
• Adequate equivalence relations and Pontryagin Products.
  Journal of Pure and Applied Algebra 196 (2005), 21-37. pdf
  
  
• Cycles on curves over global fields of positive characteristic.
  Transactions of the American Mathematical Society 357 (2005), 2557-2569. pdf
  
  
• Torsion in mixed K-groups.
  Communications in Algebra 32 (2004), 295-314. pdf
  
  
• Zero-cycles on varieties over finite fields.
  Communications in Algebra 32 (2004), 279-294. pdf
  
  
• Milnor K-theory of smooth varieties.
  K-theory 32 (2004), 269-291. pdf
  
  
• (with Alistair Lachlan) On countable homogeneous 3-hypergraphs.
  Archive for Mathematical Logic 34 (1995), 331-344.

Conference Volume

• (with P. Brosnan, R. Joshua, eds.) The Geometry of Algebraic Cycles. Papers from the 2nd Conference on Algebraic Cycles held at the Ohio State University, Columbus, OH, March 25–29, 2008. Clay Mathematics Proceedings 9.

Theses

• Milnor K-theory and zero-cycles on algebraic varieties.
  Ph.D. dissertation, Brown University (2000). pdf
  
  
• Cyclotomic Euclidean Number Fields.
  Senior thesis, Harvard University (1995). pdf

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