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on Tableaux problem 2

The statement

2.[Wor] Consider the tree $SSYT$ of shifted standard Young tableaux, with the tree structure generated by containment. Computation suggests that the only automorphism of $SSYT$ (as an unlabeled tree) is the identity. Computation further suggests that each node of $SSYT$ is uniquely determined by the census (cardinalities) of the ranks of the subtree rooted at the node.

What gets accepted

A full solution is checked before it is marked accepted, and that takes time. Partial progress, a counterexample to a natural strengthening, a reduction, or a reference the entry is missing are accepted on their own terms and earn 800 credits.

Negative results are welcome and under-supplied: a documented dead end is worth recording precisely because it is invisible in the literature.