Outline and Links for Doron Zeilberger's Talk , June 25, 2021, CIRM

  1. Thanks Cyril et. al.

  2. Warning: not a proper math talk (quote Kimmo)

  3. The triumphs of "Guess and Check":

    • Comment on MBM's talk: This simple-minded approach that ultimately lead to the FIRST proof of Gessel's conjecture, gives a (very ELEMENTARY!) one-line proof of the Kreweras walk formula (for the quarter plane) (mentioned in this masterpiece), a similar proof should exist for the three-quarter-plane.

    • Comment on Mourad I.'s talk: Christian Krathenthaler noticed that the expression of Brennan that he conjectured to be a polynomial in q, is nothing but MacMahon's box formula that immediately proves that not only are they polynomials, but they have positive coefficients. (e.g. see here)

    • Comment on Philippe Di-F's great talk. Using this nice experimental-yet-rigorous approach (that ultimately lead to the proof of the qTSPP conjecture) Christoph Koutschan proved Philippe Di-F's determinant conjecture! (that another CK could not do) (see certificate)

  4. Congratulate MBM, implicit honors

  5. Memory Lane: FPSAC 1991 (show proceedings), MBM's defense (the one who laughed, show thesis)

  6. my report

  7. shocking shortcut

  8. my rejected masterpiece (Symbolic Dynamic Programming)

  9. rebuttal

  10. Play with: TILINGS.txt

  11. Another disappointment at narrow-minded editors

  12. Play with: YoungT.txt

  13. But ALCO inspired the title of another paper (that uses Numeric Dynamical Programming) to pose deep and original questions, brilliantly answered by Michael Wallner (and thanks to him the OEIS got 100 dollars richer). So there is still room for human-generated "conceptual" math, computers can prove that something is D-finite or algebraic, but it is harder to them to suggest that something is NOT D-finite (etc.)

  14. Numeric and Symbolic Dynamical Programming for Dyck Paths enumeration

  15. Play with: Dyck.txt and DyckClever.txt

    The following links were not explored in the talk (but should have)

  16. Follow up paper by AJ BU (my brilliant current PhD student)

  17. Explore the great new Journal of Enumerative Combinatorics and Applications

  18. Another example of symbolic dynamical programming (numeric is eventually hopeless)

  19. Thanks again for a great conference!

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