On the combinatorics of tableaux -- A notebook of open problems
Dale R. Worley
TL;DR
This notebook collects open problems and a solved result in the combinatorics of tableaux, aiming to catalyze collaboration and progress. It organizes challenges from 2024 and 2025 across differential posets, automorphisms of tableau trees, limit-shape theory for generalized diagram families, and Schubert-polynomial statistics such as $\nu_w=\mathfrak{S}_w(1,\ldots,1)$. The solved entry confirms a precise link between permutation pattern avoidance and the sum of Schubert polynomial coefficients, illustrating deep connections between permutation patterns and tableau combinatorics. Overall, the work provides a structured agenda for advancing RSK-type correspondences, limit shapes, and invariants in tableau theory.
Abstract
Inspired by the the Kourovka Notebook of unsolved problems in group theory [KhukhMaz2024], this is a notebook of unsolved problems in the combinatorics of tableaux. Contributions to the notebook are invited.