Towards Heim and Neuhauser's unimodality conjecture on the Nekrasov-Okounkov polynomials

DOI10.1007/s40993-021-00244-2zbMath1460.05017arXiv2008.10069OpenAlexW3129700837WikidataQ113891359 ScholiaQ113891359MaRDI QIDQ2658350

Letong Hong, Shengtong Zhang

Publication date: 19 March 2021

Published in: Research in Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.10069

zbMATH Keywords

partitionhook formulaEuler product

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) (q)-calculus and related topics (05A30) Combinatorial aspects of partitions of integers (05A17) Analytic theory of partitions (11P82)

Related Items (3)

Log-concavity in powers of infinite series close to \((1-z)^{-1}\) ⋮ Log-concavity of infinite product and infinite sum generating functions ⋮ Fractional partitions and conjectures of Chern–Fu–Tang and Heim–Neuhauser

Uses Software

• HookExp

Cites Work

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• Log-concavity of the partition function
• Discovering hook length formulas by an expansion technique
• Log-concavity of Stirling numbers and unimodality of Stirling distributions
• On conjectures regarding the Nekrasov-Okounkov hook length formula
• The Dedekind eta function and D'Arcais-type polynomials
• Universal characters from the MacDonald identities
• Chromatic polynomials and logarithmic concavity

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