https://www2.math.upenn.edu/~wilf/website/Probabilistic%20proo | Непрерывное математическое образование

https://www2.math.upenn.edu/~wilf/website/Probabilistic%20proof.pdf

«Surprisingly, in view of the simplicity of the formula, it is difficult to explain why the hook lengths appear. (…) In the original proof hook lengths appear in the course of rearranging therms in [the Young-Frobenius formula]. The original proofs of the latter formula use complicated algebraic methods (group characters, symmetric polynomials). Another proof of the Young-Frobenius formula was found by MacMahon (…).

In this paper, we give a short direct proof. The key step is based on a probabilistic model in which hooks appear in an essential way. The method also yields an algorithm which chooses, uniformly at random, a Young tableau of given shape.»

(Greene, Nijenhuis, Wilf. A probabilistic proof of a formula for the number of Young tableaux of a given shape // Adv. Math., 1979)

начало треда: https://t.me/cme_channel/2842