Ph.D. thesis: Computer Assisted Explorations of Rogers-Ramanujan Type Identities, accepted by the Graduate School of the University of Kentucky on March 5, 2002.

Papers Accepted for Publication:

1. (with J. P. O. Santos) "q-Pell sequences and two identities of V. A. Lebesgue," Discrete Mathematics 257/1 (2002), pp. 125-143. preprint (pdf)
2. "Finite Rogers-Ramanujan type identities," Electronic Journal of Combinatorics Volume 10(1) (2003) #R13, pp. 1-122.
3. (with J. Sellers and G. Mullen) "Bijections and congruences for generalizations of partition identities of Euler and Guy," Electronic Journal of Combinatorics Volume 11(1) (2004) #R43, pp. 1-19.
4. "RRtools---a Maple package for aiding the discovery and proof of finite Rogers-Ramanujan type identities," Journal of Symbolic Computation 37/4 (2004), 415-448. Corrected proof available via Sciene Direct. preprint (pdf)
5. "A combinatorial proof of a partition identity of Andrews and Stanley," International Journal of Mathematics and Mathematical Sciences, 2004/47, 2495-2503. Preprint: pdf
6. "On identities of the Rogers-Ramanujan type," Ramanujan Journal 11 (2006), 403-429. Preprint: pdf
7. "On series expansions of Capparelli's infinite product," Advances in Applied Mathematics 33/2 (2004), 397-408. preprint
8. "Identities of the Rogers-Ramanujan-Bailey type," Journal of Mathematical Analysis and Applications 308/2 (2005), 669-688.
Preprint: pdf
9. "q-Difference Equations and identities of the Rogers-Ramanujan-Bailey type," Journal of Difference Equations and Applications 10 (2004), 1069-1084.
Preprint: pdf
10. (with D. Zeilberger) "Disturbing the Dyson conjecture (in a GOOD way)," Experimental Mathematics, 15:2 (2006), 187-191. preprint: pdf
11. "On simplifications of certain q-multisums," Advances in Applied Mathematics, to appear. preprint: pdf
12. "Disturbing the Dyson conjecture in a generally GOOD way," Journal of Combinatorial Theory, Series A 113/7 (2006) 1368-1380. preprint: pdf
13. "Identities of the Rogers-Ramanujan-Slater type," International Journal of Number Theory, to appear. preprint: pdf
14. "A partition bijection related to the Rogers-Selberg identities and Gordon's theorem," Journal of Combinatorial Theory, Series A, to appear. preprint: pdf

Mathematica Packages:

• GoodDyson.m which accompanies my joint paper with Doron Zeilberger, "Disturbing the Dyson conjecture (in a GOOD way)." Examples are available in the form of a Mathematica 5.2 notebook.
• NewZeil.m, a Mathematica implementation of the simplified Zeilberger algorithm from the Mohammed-Zeilberger paper "Sharp upper bounds for the orders of the recurrences output by the Zeilberger and q-Zeilberger algorithms", J. Symbolic Comput. 39 (2005), 201-207. Examples are available in the form of a Mathematica 5.2 notebook.

Maple Packages/Worksheets:

• RRtools and related materials:

• Download RRtools. Version 1.11, July 23, 2003. (Fully documented "RRtools---a Maple Package...")
• Download recpf. Version of April 9, 2003. The companion package of RRtools.  (Fully documented in "RRtools---a Maple Package...")
• Download the Maple V R4 worksheets containing the proofs of the identities from §3 and §6 of "Finite Rogers-Ramanujan Type Identities."
• Maple implementation of the algorithm in "Bijections and Congruences for Generalizations of Partition Identities of Euler and Guy"
• Dowload the Maple worksheet bijection.mws
Created using Maple V R4. (Works in Maple 7 and 8, but not Maple 9.)
• Maple worksheet to accompany "A Combinatorial Proof of a Partition Identity of Andrews and Stanley"
  • Download the Maple worksheet StanBij.mws
  Created using Maple 7. (Seems to work fine in Maple 9.)

• Maple package GoodDyson which accompanies my joint paper with Doron Zeilberger, "Disturbing the Dyson conjecture (in a GOOD way)." Tested on Maple 8 and 9. Seems to work properly in Maple 10 in worksheet mode. Examples are available in the form of a Maple 9 worksheet.