Publications & Pre-Prints
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Convexity at a
point, (with Serban Raianu) Bull. Math. Soc. Sci. Math. Roumanie
(N.S.) 66(114) (2023), no. 2, 235–250.
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Addendum to ``Applications of differential algebra to algebraic
independence of arithmetic functions'', Acta Arith. 196 (2020), no. 3,
325–327.
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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.
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Rank Inequalities in the Theory of Differentially Closed Fields
. Proceedings of Logic Colloquium 2003.
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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.