Some Conjectures and Open Problems on Partition Hook Lengths

DOI10.1080/10586458.2009.10128888zbMath1167.05004OpenAlexW1973949867WikidataQ123242556 ScholiaQ123242556MaRDI QIDQ5191008

Guo-Niu Han

Publication date: 28 July 2009

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.em/1243430533

zbMATH Keywords

partitionsLehmer conjecture\(t\)-coreshook length formulas

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial identities, bijective combinatorics (05A19) Combinatorial aspects of partitions of integers (05A17) Combinatorial aspects of representation theory (05E10) Counting solutions of Diophantine equations (11D45) Elementary theory of partitions (11P81)

Related Items (18)

New hook-content formulas for strict partitions ⋮ A Nekrasov-Okounkov type formula for \(\widetilde{C}\) ⋮ Multiplication theorems for self-conjugate partitions ⋮ Difference operators for partitions and some applications ⋮ Polynomiality of shifted Plancherel averages and content evaluations ⋮ Hook lengths and shifted parts of partitions ⋮ Difference operators for partitions under the Littlewood decomposition ⋮ A multiset hook length formula and some applications ⋮ Polynomiality of some hook-length statistics ⋮ Hook lengths and 3-cores ⋮ A conjecture of Han on 3-cores and modular forms ⋮ On \(t\)-core towers and \(t\)-defects of partitions ⋮ A crank-based approach to the theory of 3-core partitions ⋮ Differential operators, shifted parts, and hook lengths ⋮ On conjectures regarding the Nekrasov-Okounkov hook length formula ⋮ Unnamed Item ⋮ Combining hook length formulas and BG-ranks for partitions via the Littlewood decomposition ⋮ Polynomiality of Plancherel averages of hook-content summations for strict, doubled distinct and self-conjugate partitions

Uses Software

• HookExp

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