2023/10/27 by Darij Grinberg, Grinberg, Darij, Korniichuk, Nazar +2
Mathematics · #05A17 #05A19 #05E05 #15A15 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2310.18275
openalex publication_date 2023/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.