Hook formulas for skew shapes IV. Increasing tableaux and factorial Grothendieck polynomials
Combinatorics
2021-08-31 v2
Abstract
We present a new family of hook-length formulas for the number of standard increasing tableaux which arise in the study of factorial Grothendieck polynomials. In the case of straight shapes our formulas generalize the classical hook-length formula and Stanley's formula. For skew shapes, our formulas generalize the Naruse hook-length formula and its -analogues, which were studied in previous papers of the series.
Keywords
Cite
@article{arxiv.2108.10140,
title = {Hook formulas for skew shapes IV. Increasing tableaux and factorial Grothendieck polynomials},
author = {Alejandro H. Morales and Igor Pak and Greta Panova},
journal= {arXiv preprint arXiv:2108.10140},
year = {2021}
}
Comments
26 pages, 3 figures. This is the fourth paper in the series "Hook formulas for skew shapes", v2. expanded final remarks, added section 6.4 with a generalization of the Okounkov-Olshanski formula, fixed typos