Publications & Pre-Prints

My MathSciNet profile

Publications

• Convexity at a point, (with Serban Raianu) Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 66(114) (2023), no. 2, 235–250.
• Densities of length spectral partitions of natural numbers (with BEnjamin Garcia Morales) Online Journal of Analytic Combinatorics, Issue 17, 2022.
• Addendum to ``Applications of differential algebra to algebraic independence of arithmetic functions'', Acta Arith. 196 (2020), no. 3, 325–327.
• Refinement of Metrics: Erdos Numbers, a Case Study, (with Kayla Lock and Alexander Wittmond) the PUMP Journal of Undergraduate Research, 2, 118-130, Aug, 2019.
• Applications of differential algebra to algebraic independence of arithmetic functions (version on arivx with an addenum), Acta Arith. 172 (2016), no. 2, 149-173.
• Diophantine Equations of Matching Games II (with Roel Stroeker), Acta Arithmetica. 151 (2012) no. 3, pages 311--323.
• Diophantine Equation of Mathching Games I (with Chun Yin Hui), INTEGERS, Volume 12, issue 2, (2012), pages 179--195
• Quantifier Eliminable Locally Finite Graphs (with Shawn Hedman), Mathematical Logic Quarterly Volume 57, Issue 2, April 2011.
• Locally Finite Homogeneous Graphs (with Shawn Hedman), Combinatorica, Volume 30 Issue 4, July 2010.
• Length Spectra of Natural Numbers, International Journal of Number Theory, Volume: 5, Issue: 6(2009) pp. 1089-1102.
• Sums of Consecutive Integers, the College Mathematics Journal, Vol. 38, NO. 2, March 2007, p.119–123.
• Rank Inequalities in the Theory of Differentially Closed Fields . Proceedings of Logic Colloquium 2003.
• Orderings of Monomial ideals (with Matthias Aschenbrenner).Fund. Math. 181 (2004), no. 1, 27--74.
• On Lascar Rank and Morley Ranks of definable groups in differentially closed fields, (with Anand Pillay), Journal of Symbolic Logic. Volume 67. Number 3. Sept. 2002.
• On a result of Rosenlicht. May 2000. Communications in Algebra, Vol. 30, issue 12, 2002, p.5933-5939.
• Chains of Differential Subvarieties of an Algebraic Variety. Journal of Algebra 248, 755-764, 2002.
• Some Applications of Ordinal Dimensions to the Theory of Differentially Closed Fields. Journal of Symbolic Logic. (2000), 65, no. 1, pp.347-356.
• Complete Sets in Differentially Closed Fields. Journal of Algebra 224, 454-466 (2000).
• Ordinal Dimensions and Completeness in Differentially Closed Field. Thesis. May 1999.

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