The (ordinary) generating functions enumerating \(123\)-avoiding words with \(r\) occurrences of each of \(1, 2, \dots, n\) are always algebraic (Q295298)
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scientific article; zbMATH DE number 6592719
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The (ordinary) generating functions enumerating \(123\)-avoiding words with \(r\) occurrences of each of \(1, 2, \dots, n\) are always algebraic |
scientific article; zbMATH DE number 6592719 |
Statements
The (ordinary) generating functions enumerating \(123\)-avoiding words with \(r\) occurrences of each of \(1, 2, \dots, n\) are always algebraic (English)
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13 June 2016
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The authors generalize a result of \textit{W. Y. C. Chen} et al. [Eur. J. Comb. 36, 416--424 (2014; Zbl 1284.05034)]. From the authors' abstract: ``(W)e present an algorithm for finding\dots an algebraic equation for the ordinary generating function enumerating 123-avoiding words with exactly \(r\) occurrences of each of \(\{1,2,\dots,n\}\) for \textit{any} positive integer \(r\), thereby proving that they are \textit{algebraic}.''
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pattern avoidance
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words
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algebraic generating functions
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