Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí toán học quốc tế đề tài: Finite Rogers-Ramanujan Type Identities | Finite Rogers-Ramanujan Type Identities Andrew V. Sills through August 2003 Department of Mathematics The Pennsylvania State University University Park PA USA sills@ http sills starting September 2003 Department of Mathematics Rutgers University Hill Center Busch Campus Piscataway NJ USA sills@ http sills Submitted May 14 2002 Revised Aug 27 2002 Accepted Apr 10 2003 Published Apr 23 2003 MR Subject Classifications 05A10 11B65 Abstract 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. The author has implemented much of the finitization process in a Maple package which is available for free download from the author s website. 0 Introduction Three approaches to finitization There are at least three avenues of approach that lead to finite Rogers-Ramanujan type identities. The research contained herein comprises a substantial portion of the author s doctoral dissertation submitted in partial fulfillment of the requirements for the . degree at the University of Kentucky. The doctoral dissertation was completed under the supervision of George E. Andrews Evan Pugh Professor of Mathematics at the Pennsylvania State University. This research was partially supported by a grant provided to the author by Professor Andrews. THE ELECTRONIC JOURNAL OF COMBINATORICS 10 2003 R13 1 1. Combinatorics and models from statistical mechanics. This approach has been studied extensively by Andrews Baxter Berkovich Forrester McCoy Schilling War-naar and others see . 7 15 16 18 17 27 30 31 36 63 70 71 72 . 2. The Strong Bailey Lemma. This method is discussed in chapter 3 of Andrews q-series monograph 10 . 3. The method of nonhomogeneous q-difference equations. This method is .
