Young tableau reconstruction via minors
William Q. Erickson, Daniel Herden, Jonathan Meddaugh, Mark R., Sepanski, Cordell Hammon, Jasmin Mohn, Indalecio Ruiz-Bolanos

TL;DR
This paper investigates the tableau reconstruction problem using minors, proving a sharp lower bound for reconstructing standard Young tableaux from their 2-minors and exploring bounds for multisets of minors.
Contribution
The paper extends previous work by solving the tableau reconstruction problem for 2-minors and providing initial bounds for multisets of minors.
Findings
Reconstruction from 2-minors is possible for tableaux of size at least 8.
Established a lower bound for multiset minors reconstruction for arbitrary k.
Solved the problem for k=2, complementing the known solution for k=1.
Abstract
The tableau reconstruction problem, posed by Monks (2009), asks the following. Starting with a standard Young tableau , a 1-minor of is a tableau obtained by first deleting any cell of , and then performing jeu de taquin slides to fill the resulting gap. This can be iterated to arrive at the set of -minors of . The problem is this: given , what are the values of such that every tableau of size can be reconstructed from its set of -minors? For , the problem was recently solved by Cain and Lehtonen. In this paper, we solve the problem for , proving the sharp lower bound . In the case of multisets of -minors, we also give a lower bound for arbitrary , as a first step toward a sharp bound in the general multiset case.
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Taxonomy
TopicsDigital Image Processing Techniques
