Timeline for Hook lengths, contents and recurrence
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 16, 2021 at 18:39 | answer | added | T. Amdeberhan | timeline score: 1 | |
| Mar 15, 2021 at 21:15 | comment | added | Gjergji Zaimi | The generating function via Littlewood's identity was discussed here mathoverflow.net/questions/263643 | |
| Mar 15, 2021 at 20:56 | comment | added | Sam Hopkins | So together with @user61318's observation, Ira's formula follows from Stanley's Hook Content Formula. By the way for discussion of Littlewood's identity, in fact "bounded" versions of it, see arxiv.org/abs/1506.02755. | |
| Mar 15, 2021 at 20:49 | comment | added | user35313 | The generating function mentioned by Ira Gessel is the specialization of an identity of Littlewood: on one side is the sum of all Schur polynomials in a finite fixed set of variables and on the other side $\prod_{1\leq i\leq n}(1-x_i)^{-1}\prod_{1\leq i<j\leq n}(1-x_ix_j)^{-1}$. So $f_n(t)$ is counting semistandard tableau according to their evaluations (the other meaning of content). | |
| Mar 15, 2021 at 20:27 | comment | added | Ira Gessel | It seems that $$\sum_{n=0}^\infty f_n(t) x^n = \frac{1}{(1-x)^t (1-x^2)^{\binom{k}{2}}}.$$ | |
| Mar 15, 2021 at 19:41 | history | edited | Per Alexandersson | CC BY-SA 4.0 |
fixed misspelled title
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| Mar 15, 2021 at 19:30 | history | asked | T. Amdeberhan | CC BY-SA 4.0 |