Reconstructing Young Tableaux

Reconstruction problems ask whether a mathematical object is uniquely determined by a collection of pieces of partial information about the object. A classical example of such a problem is whether every finite simple graph with at least three vertices is uniquely determined by the collection of its one-vertex-deleted induced subgraphs.

The analogous question for partitions was settled independently by Monks (2009) and Vatter (2008). Monks also posed the question: for which n and k is each standard Young tableaux of size n uniquely determined by the set of all tableaux obtained by deleting k entries using "jeu de taquin"? No progress had been made on this question until recently.

This talk will describe the first steps towards answering this and related questions, including a complete characterization of those standard Young tableaux that are uniquely determined by the set of all tableaux obtained by deleting 1 entry.

This is joint work with Erkko Lehtonen.