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- W4221146394 abstract "Motivated by the many roles that hook lengths play in mathematics, we study the distribution of the number of $t$-hooks in the partitions of $n$. We prove that the limiting distribution is normal with mean $mu_t(n)sim frac{sqrt{6n}}{pi}-frac{t}{2}$ and variance $sigma_t^2(n)sim frac{(pi^2-6)sqrt{6n}}{2pi^3}.$ Furthermore, we prove that the distribution of the number of hook lengths that are multiples of a fixed $tgeq 4$ in partitions of $n$ converge to a shifted Gamma distribution with parameter $k=(t-1)/2$ and scale $theta=sqrt{2/(t-1)}.$" @default.
- W4221146394 created "2022-04-03" @default.
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- W4221146394 date "2022-01-17" @default.
- W4221146394 modified "2023-10-17" @default.
- W4221146394 title "Distributions of Hook lengths in integer partitions" @default.
- W4221146394 doi "https://doi.org/10.48550/arxiv.2201.06630" @default.
- W4221146394 hasPublicationYear "2022" @default.
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