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Ask Not What Doron Zeilberger Can Do For You, Ask What You Can Do For Doron Zeilberger Part 1

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Uploaded on Jun 9, 2010

Aviezri Fraenkel, Weizmann Institute of Science, Israel
Title: Ask Not What Doron Zeilberger Can Do For You, Ask What You Can Do For Doron Zeilberger

Two conjectures on multi-pile Wythoff's game that I once mentioned to Doron Zeilberger, were proved by him and Xinyu Sun very elegantly for the special case of 3 piles where the smallest pile has size at most 10, demonstrating that if you do something for Doron, you get a 10-fold reward! Their approach has the potential for an infinity-fold reward. We review the conjectures, the fractal-like structure of some complementary sets of integers connected with them (joint with Dalia Krieger), and new results and problems on complementary sets (in part joint with Peter Hegarty and Urban Larsson).

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