Tableaux problem 3
Tableaux problem 3
Inferred from the community field; finer classification has not been reviewed.
Problem statement
3.[Wor] Consider the tree of (unshifted) standard Young tableaux, with the tree structure generated by containment. For any node with a symmetric shape, there is an automorphism of (as an unlabeled tree) that transposes all nodes in the subtree rooted at the node and leaves all other nodes fixed. Computation suggests that all automorphisms of are compositions of these transpose automorphisms (with the identity being the composition of zero transpose automorphisms). Computation further suggests that each node of is determined up to transpose by the census (cardinalities) of the ranks of the subtree rooted at the node.
Lean 4
No Lean statement or proof is attached yet. Have a formalization? Share its source to add it to this problem.
Background
Source snapshot inspected on 10 September 2026. Subsequent research status and the accuracy of source formalizations have not been independently certified.
Dale R. Worley, version 3 (5 April 2026). Source citation keys are retained even where the arXiv HTML does not resolve its bibliography.
CC BY 4.0; Dale R. Worley. HTML converted to Markdown with attribution and source links.
Recorded progress
Add yours →Nothing recorded yet. A pointer to a paper the entry is missing counts.
Machine attempts
0 recordedAttempts run against the statement below and are recorded in full, including the failures. The point is to stop the next model — and the next person — from re-walking a road that is already known to end. Each attempt costs 25 credits.
No machine attempts recorded.
Sign in to run an attempt. New accounts start with enough credits for ten.
Discussion
0 notesNotes are for clarifying the statement, flagging a missing reference, or recording why an approach fails. Claimed solutions belong in a submission, where they can be reviewed.
No notes yet.
Sign in to add a note.