Proof of a Conjecture about Multisets of Hook Numbers

By Amitai Regev and Doron Zeilberger

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(Appaered in Annals of Combinatorics 1(1997), 391-394)).

The Hook-Length Formula, or rather its proof by Greene-Nijenhuis-Wilf (Adv. Math. 31(1979), 104-109), was the single most influential event that got me totally HOOKED and led to my conversion from analysis to combinatorics.

Hence, it is not surprising that when Amitai Regev told me about his fascinating conjecture (with Anatoly Vershik) about certain multisets of hook numbers, I was HOOKED once again. Amitai and I started working on this problem during my last visit (Aug. 1997) to the Weizmann Institute, and after a few more E-mails, once I got back, we finished up the problem.

Note Added Oct. 16: Svante Janson has independently obtained the results in this paper.

Note added Jan. 28, 1999: Jeniffer Galovich found a typo in the definition of hook at the beginning of the paper: the relation between i and i' and j and j' should be reversed.

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