English

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 qq-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