On the spiral property of the \(q\)-derangement numbers (Q1126223)
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scientific article; zbMATH DE number 955108
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the spiral property of the \(q\)-derangement numbers |
scientific article; zbMATH DE number 955108 |
Statements
On the spiral property of the \(q\)-derangement numbers (English)
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8 December 1996
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\textit{W. Y. Chen} and \textit{G.-C. Rota} [Discrete Math. 104, No. 1, 7-22 (1992; Zbl 0806.05010)] adduced the following conjecture about the \(q\)-derangement numbers \(D_n(q)\) (proved to be unimodal): the maximum coefficient in \(D_n(q)\) is that of \(q^{\lceil n(n-1)/4\rceil}\). The author proves this conjecture, discovering `the spiral property' in decrease of the coefficients from the middle.
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\(q\)-analogues
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unimodal polynomial
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\(q\)-derangement numbers
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coefficient
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