This page is a collection of my research writings. Currently i am an honorary research fellow in the University of Auckland Computer Science Department.

Previously (2006.05--2009.04) i worked as a postdoctoral research fellow in the University of Auckland Computer Science Department with Mark Wilson in the area of mathematics: combinatorics: enumerative combinatorics (Mathematics Subject Classification 05A15, 05A16; subscription required). More specifically, we studied asymptotics of Maclaurin coefficients of multivariate generating functions.

Publications

Most of the articles below are the journal versions but typeset without the journal house styles and with minor typos corrected.

• amgf.sage. Current version under "Sage Files" below. Sage code for the computation of asymptotics of Maclaurin coefficients of multivariate generating functions, submitted.
• Asymptotics of coefficients of multivariate generating functions: improvements for multiple points. Alexander Raichev and Mark C. Wilson, to appear in Online Journal of Analytic Combinatorics, issue 2011. Accompanying Sage worksheet below.
• Asymptotics of coefficients of multivariate generating functions: improvements for smooth points. Alexander Raichev and Mark C. Wilson, Electronic Journal of Combinatorics, Vol. 15 (2008), R89. Update 2008.10.20: minor typos corrected.
• A new method for computing asymptotics of diagonal coefficients of multivariate generating functions. Alexander Raichev and Mark C. Wilson, Discrete Mathematics & Theoretical Computer Science Proceedings, Conference on Analysis of Algorithms 2007.
• A minimal rK-degree. Alexander Raichev and Frank Stephan, Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, Vol. 15 (2008), 261--269.
• Model completeness for trivial, uncountably categorical theories of Morley rank 1. Alfred Dolich, Michael C. Laskowski, and Alexander Raichev, Archive for Mathematical Logic, Jul 2006, 1--15.
• Relative randomness and real closed fields. Alexander Raichev, Journal of Symbolic Logic, 70 (2005), no. 1, 319--330.
  Were i to write this paper and the corresponding section in my thesis again, i would use the standard notion of a computable real function instead of introducing the new notion of a weakly computable real function, and then use computable locally Lipschitz functions. The theorems all go through with only minor modifications.
• Relative randomness and real closed fields (extended abstract). Proceedings of the 6th Workshop on Computability and Complexity in Analysis (CCA 2004), 135--143, Electron. Notes Theor. Comput. Sci., 120, Elsevier, Amsterdam, 2005.

Sage Files

Sage is a free, open-source alternative to Magma, Maple, Mathematica and Matlab. You can read more about it at sagemath.org.

• amgf-0.6.1.alpha.sage. Version date 27 June 2011. To be incorporated piece-by-piece into the Sage codebase. Currently under peer review on the Sage Trac server. Let me know if you find any bugs or have any comments. Instructions:
  1. Download and install the latest version of Sage from sagemath.org.
  2. Run Sage and open a notebook window. (Type 'notebook()' if you are running Sage from the command line.)
  3. Download the accompanying amgf worksheet below and load it into your notebook.
  4. Run the worksheet and modify the examples to your liking.
• amgf-0.6.1.alpha examples.sws. Sage worksheet that contains examples from the articles "Asymptotics of coefficients of multivariate generating functions: improvements for smooth points" and "Asymptotics of coefficients of multivariate generating functions: improvements for multiple points" above.

Slides

• Analytic combinatorics: asymptotics for multivariate meromorphic functions. (Also known as "Don't need any license to be handled any vehicles".) Presented 2007.12.07 at the 32nd Australasian Conference on Combinatorial Mathematics & Combinatorial Computing (32ACCMCC), University of Otago, New Zealand.
• A new diagonal method. Presented 2007.06.22 at the 2007 Conference on Analysis of Algorithms (AofA'07), Juan les Pins, France.

Ph.D. Thesis

• Relative randomness via rK-reducibility. A dissertation in the area of mathematics: logic: computability theory: algorithmic randomness (Mathematics Subject Classification 03D30, 68Q30; subscription required). Completed at the University of Wisconsin-Madison Mathematics Department under the guidance of Steffen Lempp. Defended 2006.02.14. Update 2006.05.13: minor correction made to Section 2.1.

Curriculum Vitae

Here.