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Preprint (Author's original)arXiv.org - Non-exclusive license to distribute, Open
Preprint
The Pak--Postnikov and Naruse skew hook length formulas: a new proof
arXiv.org
27 Oct 2023
Abstract
The classical hook length formula of enumerative combinatorics expresses the
number of standard Young tableaux of a given partition shape as a single
fraction. In recent years, two generalizations of this formula have emerged:
one by Pak and Postnikov, replacing the number by a (rational) generating
function, and one by Naruse, which generalizes the setting from a partition to
a skew partition. Both generalizations appear to lie significantly deeper, with
no simple proofs known. We combine them into a generating-function identity for
skew partitions, and prove it in a fairly elementary way using recursion,
determinants and simple combinatorics.
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Details
- Title
- The Pak--Postnikov and Naruse skew hook length formulas: a new proof
- Creators
- Darij GrinbergNazar KorniichukKostiantyn MolokanovSeveryn Khomych
- Publication Details
- arXiv.org
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991021862368604721