Hook formulas for skew shapes

The celebrated hook-length formula gives a product formula for the number of standard Young tableaux of a straight shape. In 2014, Naruse announced a more general formula for the number of standard Young tableaux of skew shapes as a positive sum over excited diagrams of products of hook-lengths. We...

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Bibliographic Details
Published inDiscrete Mathematics and Theoretical Computer Science Vol. DMTCS Proceedings, 28th...
Main Authors Morales, Alejandro H., Pak, Igor, Panova, Greta
Format Journal Article Conference Proceeding
LanguageEnglish
Published DMTCS 22.04.2020
Discrete Mathematics & Theoretical Computer Science
Subjects
[math.math-co]mathematics [math]/combinatorics [math.co]
Combinatorics
Mathematics
Combinatorics
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Summary:The celebrated hook-length formula gives a product formula for the number of standard Young tableaux of a straight shape. In 2014, Naruse announced a more general formula for the number of standard Young tableaux of skew shapes as a positive sum over excited diagrams of products of hook-lengths. We give two q-analogues of Naruse's formula for the skew Schur functions and for counting reverse plane partitions of skew shapes. We also apply our results to border strip shapes and their generalizations.
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.46298/dmtcs.6354