============================== Bar-Ilan Combinatorics Seminar ============================== The next meeting of the seminar will take place, IYH, on (when) Tuesday, 10 Sivan (June 2) 13:00-14:30 *** NOTE UNUSUAL HOUR *** (where) Room 201 (Math Dept Seminar Room), Math and CS Building (216), Bar-Ilan University (who) Steve Tanny (University of Toronto) will talk about (what) "Meta-Fibonacci recursions: Hofstadter, Conolly and much more" Abstract: The study of integer sequences defined by meta-Fibonacci recursions (also called self-referencing or nested recursions) is a promising new field that has grown in the last thirty years from a brief mention in Hofstadters book Godel, Escher, Bach: An Eternal Golden Braid to dozens of papers by mathematicians around the world. In these recursions the arguments in the function defining the sequence depend upon earlier values of the sequence itself. In this talk we provide some general background on these recursions. We then discuss various generalizations of the Conolly meta-Fibonacci recursion, defined by C(n) = C(n-C(n-1)) + C(n-1-C(n-2)), with initial conditions C(1) = C(2) = 1. Our focus is on variants of the Conolly recursion, together with their corresponding initial conditions, that generate sequences that are slowly growing. These are sequences that are monotone non-decreasing and whose successive terms differ by 0 or 1. In certain cases, we are able to derive a fascinating and unexpected combinatorial interpretation for such sequences: we show that they count the number of leaves in certain sub-trees of infinite trees, including binary trees, with special labeling schemes. Forthcoming Events: ------------------- * 17 Sivan (June 9) Ohad Feldheim (Tel-Aviv University): "Non-backtracking walks and the eigenvalues of random matrices" * 24 Sivan (June 16) Shachar Lovett (Weizmann Institute): "List-decoding Reed-Muller codes" ************************************************************************* You are all invited ! (Graduate students especially welcome) If you want to give a talk at the seminar, or know a prospective speaker, please contact Ron Adin . Seminar's homepage: *************************************************************************