Andrew Sills
Professor of Mathematics Georgia Southern University
- Statesboro/Savannah GA
Andrew Sills specializes in number theory and combinatorics and currently leads the computational sciences group in COSM.
Media
Areas of Expertise
Education
University of Kentucky
Ph.D.
Mathematics
2002
The Pennsylvania State University
M.A.
Mathematics
1994
Rutgers University
B.A.
Mathematics
1989
Affiliations
- American Mathematical Society
- Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)
- American Statistical Association
Articles
Ghost series and a motivated proof of the Andrews–Bressoud identities
Journal of Combinatorial Theory, Series AKanade, Shashank; Lepowsky, James; Russell, Matthew C.; Sills, Andrew V.
2017
We present what we call a “motivated proof” of the Andrews–Bressoud partition identities for even moduli. A “motivated proof” of the Rogers–Ramanujan identities was given by G.E. Andrews and R.J. Baxter, and this proof was generalized to the odd-moduli case of Gordon's identities by J. Lepowsky and M. Zhu. Recently, a “motivated proof” of the somewhat analogous Göllnitz–Gordon–Andrews identities has been found.
Rademacher's infinite partial fraction conjecture is (almost certainly) false
Journal of Difference Equations and ApplicationsAndrew V. Sills & Doron Zeilberger
2013
In his book Topics in Analytic Number Theory, Hans Rademacher conjectured that the limits of certain sequences of coefficients that arise in the ordinary partial fraction decomposition of the generating function for partitions of integers into at most N parts exist and equal particular values that he specified. Despite being open for nearly four decades, little progress has been made towards proving or disproving the conjecture, perhaps in part due to the difficulty in actually computing the coefficients in question.
Ramanujan-Slater type identities related to the moduli 18 and 24
Journal of Mathematical Analysis and ApplicationsAndrew V. Sills & James McLaughlin
2008
We present several new families of Rogers-Ramanujan type identities related to the moduli 18 and 24. A few of the identities were found by either Ramanujan, Slater, or Dyson, but most are believed to be new. For one of these families, we discuss possible connections with Lie algebras. We also present two families of related false theta function identities.
Identities of the Rogers-Ramanujan-Slater type
Int. J Number Theory 3Andrew V. Sills
2007
It is shown that (two-variable generalizations of) more than half of Slater's list of 130 Rogers–Ramanujan identities (L. J. Slater, Further identities of the Rogers–Ramanujan type, Proc. London Math Soc. (2)54 (1952) 147–167) can be easily derived using just three multiparameter Bailey pairs and their associated q-difference equations. As a bonus, new Rogers–Ramanujan type identities are found along with natural combinatorial interpretations for many of these identities.
Disturbing the Dyson conjecture, in a generally GOOD way
Journal of Combinational Theory, Series AAndrew V. Sills
2006
In this paper, closed form expressions are given for the coefficients of several other terms in the Dyson product, and are proved using an extension of Good's idea. Also, conjectures for the corresponding q-analogs are supplied. Finally, perturbed versions of the q-Dixon summation formula are presented.
Finite Rogers-Ramanujan type identities
Electron J. CombinAndrew V. Sills
2003
Polynomial generalizations of all 130 of the identities in Slater's list of identities of the Rogers-Ramanujan type are presented. Furthermore, duality relationships among many of the identities are derived. Some of the these polynomial identities were previously known but many are new.
