Young tableau reconstruction via minors
Year: 2024
Type: article
Abstract: The tableau reconstruction problem, posed by Monks (2009), asks the following. Starting with a standard Young tableau T , a 1-minor of T is a tableau obtained by first deleting any cell of T , and then performing jeu de taquin slides to fill the resulting gap. This can be iterated to arrive at the set of k -minors of T . The problem is this: given k , what are the values of n such that every tableau of size n can be reconstructed from its set of k -minors? For k = 1 , the problem was recently solved by Cain and Lehtonen. In this paper, we solve the problem for k = 2 , proving the sharp lower bound n ≥ 8 . In the case of multisets of k -minors, we also give a lower bound for arbitrary k , as a first step toward a sharp bound in the general multiset case.
Institution: Baylor University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,450
OpenAlex ID: W4401872456