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Zapiski Nauchnykh Seminarov POMI, 2021, Volume 507, Pages 59–98
(Mi znsl7161)
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Hook formulas for skew shapes IV. Increasing tableaux and factorial Grothendieck polynomials
A. H. Moralesa, I. Pakb, G. Panovac a Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003, USA
b Department of Mathematics, University of California, Los Angeles, CA 90095, USA
c Department of Mathematics, University of Southern California, Los Angeles, CA 90089, USA
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 the Littlewood formula. For skew shapes, our formulas generalize the Naruse hook-length formula and its $q$-analogs, which were studied in previous papers of the series.
Key words and phrases:
hook-length formula, factorial symmetric functions, Grothendieck polynomials, standard Young tableaux, increasing tableaux.
Received: 29.08.2021
Citation:
A. H. Morales, I. Pak, G. Panova, “Hook formulas for skew shapes IV. Increasing tableaux and factorial Grothendieck polynomials”, Representation theory, dynamical systems, combinatorial methods. Part XXXIII, Zap. Nauchn. Sem. POMI, 507, POMI, St. Petersburg, 2021, 59–98
Linking options:
https://www.mathnet.ru/eng/znsl7161 https://www.mathnet.ru/eng/znsl/v507/p59
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Abstract page: | 59 | Full-text PDF : | 9 | References: | 11 |
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