A representation theorem for (\(q\)-)holonomic sequences (Q386034)
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scientific article; zbMATH DE number 6238120
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A representation theorem for (\(q\)-)holonomic sequences |
scientific article; zbMATH DE number 6238120 |
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A representation theorem for (\(q\)-)holonomic sequences (English)
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13 December 2013
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holonomic sequencies
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\(q\)-holonomic sequenes
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positional weights on words
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regular languages
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sparse regular languages
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monadic second-order logic
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0.8995452
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0.87915146
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0.87517375
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0.86330646
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0.8614137
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0.85919803
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The authors are interested in two families of sequences: holonomic sequences, i.e., sequences satisfying linear recurrence relations with polynomial coefficients, and their \(q\)-analogs, called \(q\)-holonomic sequences. More precisely, their purpose is to generalize the famous Chomsky-Schützenberger theorem, which implies that every sequence satisfying a linear recurrence relation with constant coefficients can be obtained as the difference of two counting functions of regular languages.NEWLINENEWLINE The authors give representation theorems for both holonomic and \(q\)-holonomic sequences. Furthermore, they give a representation theorem for holonomic sequences that does not use regular but sparse regular languages.
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