In OEIS sequence A001405, Mike Zabrocki claims that the number of Standard Young Tableaux of length $\leq 2$ is equal to $\binom{n}{\lfloor n/2 \rfloor}$.

I haven't been able to conjure up a bijection. Is there a standard bijection to know about?

  • $\begingroup$ I think it must have to do with ballot sequences. See the two notes by Joerg Arndt on A000085. $\endgroup$ – saulspatz Mar 8 at 3:39
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    $\begingroup$ There's a (non-bijective) proof here: amsacta.unibo.it/2443/1/bounded_height.pdf ; it also contains a reference to what seems to be the original representation-theoretic proof. $\endgroup$ – Marcus M Mar 8 at 15:52

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