Reconstructing Young Tableaux

TL;DR

This paper provides a complete characterization of which standard Young tableaux can be reconstructed from their sets or multisets of 1-minors, showing that most tableaux with at least 5 entries are uniquely reconstructible.

Contribution

It introduces a full characterization of reconstructibility of Young tableaux from 1-minors, advancing understanding of their combinatorial properties.

Findings

Most standard Young tableaux with at least 5 entries are reconstructible from their 1-minors.

The paper characterizes all tableaux that can be reconstructed from their 1-minors.

Reconstruction is possible for all tableaux with at least 5 entries.

Abstract

This paper completely characterizes the standard Young tableaux that can be reconstructed from their sets or multisets of $1$-minors. In particular, any standard Young tableau with at least $5$ entries can be reconstructed from its set of $1$-minors.