----------------- From sprugnoli@dsi.unifi.it Mon Jul 17 06:44:34 2006 To: zeilberg@math.rutgers.edu From: Renzo Sprugnoli Dear Prof. Zeilberger, we met many years ago (1991) in Montreal, during a Formal Power Series and Algebraic Combinatorics Conference. Since then, I followed your research activity, especially for what concerns your methods for hypergeometric summation. My scientific origin is Computer Science, so I can understand your opinions on the role of computers (and programming) in Mathematics, although I do not completely agree with your philosophical positions. Some days ago, my colleague Donatella Merlini draw my attention on your comments on the rejection of your paper "Automatic CounTilings". I can understand your reaction and I agree with you, when you say that the referee was not qualified. Actually, we worked for several years on tiling problems and published our papers in qualified serials, but people seems to be more interested in solving single problems, rather than in developing general methodologies. Our main paper on this subject is: D. Merlini, R. Sprugnoli, M. C. Verri "Strip tiling and regular grammars", published on Theoretical Computer Science, Volume 242 (2000) p. 109-124. The content of that paper is just the same as yours, apart from a minor point: we only consider connected pieces. The paper was the result of a Maple program, which solves any tiling problem relative to a strip of fixed width $p$ and indefinite length $n$. Successively, we produced a C++ version of the program to gain efficiency, and we obtained some fine results on tiling with Tetris pieces. We arrived up to $p=8$, just because the problem is NP-complete and its complexity grows exponentially with $p$ (and the number of different pieces). These results are given in the paper by Martinelli, Merlini, Rocchini, Romoli, Verri, "A software to Solve Strip Tiling Problems ", Lecture Notes in Computers Science, 12-th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC00), Moscow (Russia), (2000). Other results are contained in the paper by Merlini, Sprugnoli, Verri, "A strip-like tiling algorithm", Theoretical Computer Science, 282 (2): 337-352, 2002. Curiously, they were first presented at a Conference "Fun with Agorithms", held at Elba Isle. You can download these articles and the relative programs from Prof. Merlini's site: http://www.dsi.unifi.it/~merlini/ I thank you for your attention and remain sincerely yours Renzo Sprugnoli -------------------------------------- oooooooooooooooooooooooooooooooooooooo Prof. Renzo Sprugnoli Dipartimento di Sistemi e Informatica Viale Morgagni, 65 50134 FIRENZE Tel. 055-4237438 Fax 055-4237436 e-mail: sprugnoli@dsi.unifi.it