Analytic aspects of the shuffle product

Authors Marni Mishna, Mike Zabrocki

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Marni Mishna
Mike Zabrocki

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Marni Mishna and Mike Zabrocki. Analytic aspects of the shuffle product. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 561-572, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)


There exist very lucid explanations of the combinatorial origins of rational and algebraic functions, in particular with respect to regular and context free languages. In the search to understand how to extend these natural correspondences, we find that the shuffle product models many key aspects of D-finite generating functions, a class which contains algebraic. We consider several different takes on the shuffle product, shuffle closure, and shuffle grammars, and give explicit generating function consequences. In the process, we define a grammar class that models D-finite generating functions.
  • Generating functions
  • formal languages
  • shuffle product


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