Saturation property fails for Schubert coefficients
Combinatorics
2026-01-08 v1
Abstract
The saturation property for Littlewood--Richardson coefficients was established by Knutson and Tao in 1999. In 2004, Kirillov conjectured that the saturation property extends to Schubert coefficients. We disprove this conjecture in a strong form, by showing that it fails for a large family of instances. We also refute the saturation property for Schubert coefficients under bit scaling and discuss computational complexity implications.
Keywords
Cite
@article{arxiv.2601.04182,
title = {Saturation property fails for Schubert coefficients},
author = {Igor Pak and Colleen Robichaux},
journal= {arXiv preprint arXiv:2601.04182},
year = {2026}
}
Comments
13 pages