Asymptotics for skew standard Young tableaux via bounds for characters
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- by Jehanne Dousse and Valentin Féray PDF
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Abstract:
We are interested in the asymptotics of the number of standard Young tableaux $f^{\lambda /\mu }$ of a given skew shape $\lambda /\mu$. We mainly restrict ourselves to the case where both diagrams are balanced, but investigate all growth regimes of $|\mu |$ compared to $|\lambda |$, from $|\mu |$ fixed to $|\mu |$ of order $|\lambda |$. When $|\mu |=o(|\lambda |^{1/3})$, we get an asymptotic expansion to any order. When $|\mu |=o(|\lambda |^{1/2})$, we get a sharp upper bound. For larger $|\mu |$, we prove a weaker bound and give a conjecture on what we believe to be the correct order of magnitude.
Our results are obtained by expressing $f^{\lambda /\mu }$ in terms of irreducible character values of the symmetric group and applying known upper bounds on characters.
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Additional Information
- Jehanne Dousse
- Affiliation: Institut für Mathematik, Universität Zürich, Winterthurerstr. 190, CH-8032 Zürich, Switzerland
- Address at time of publication: CNRS, Universite Claude Bernard Lyon 1, UMR5208, Institut Camille Jordan, F-69622 Villeurbanne, France
- MR Author ID: 1036858
- ORCID: 0000-0001-6825-0389
- Email: dousse@math.cnrs.fr
- Valentin Féray
- Affiliation: Institut für Mathematik, Universität Zürich, Winterthurerstr. 190, CH-8032 Zürich, Switzerland
- Email: valentin.feray@math.uzh.ch
- Received by editor(s): January 31, 2018
- Received by editor(s) in revised form: January 18, 2019
- Published electronically: May 9, 2019
- Additional Notes: Both authors were partially supported by grant SNF-149461 from the Swiss National Science Foundation.
- Communicated by: Patricia L. Hersh
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 4189-4203
- MSC (2010): Primary 05A16, 05E05, 05E10
- DOI: https://doi.org/10.1090/proc/14558
- MathSciNet review: 4002535