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Binomial Coefficients, Valuations, and Words

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Developments in Language Theory (DLT 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10396))

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Abstract

The study of arithmetic properties of binomial coefficients has a rich history. A recurring theme is that p-adic statistics reflect the base-p representations of integers. We discuss many results expressing the number of binomial coefficients \(\left( {\begin{array}{c}n\\ m\end{array}}\right) \) with a given p-adic valuation in terms of the number of occurrences of a given word in the base-p representation of n, beginning with a result of Glaisher from 1899, up through recent results by Spiegelhofer–Wallner and Rowland.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Hofstra University, Hempstead, NY, 11549, USA

    Eric Rowland

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  1. Eric Rowland
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Correspondence to Eric Rowland .

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Editors and Affiliations

  1. Université de Liège, Liège, Belgium

    Émilie Charlier

  2. Université de Liège, Liège, Belgium

    Julien Leroy

  3. Université de Liège, Liège, Belgium

    Michel Rigo

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Rowland, E. (2017). Binomial Coefficients, Valuations, and Words. In: Charlier, É., Leroy, J., Rigo, M. (eds) Developments in Language Theory. DLT 2017. Lecture Notes in Computer Science(), vol 10396. Springer, Cham. https://doi.org/10.1007/978-3-319-62809-7_3

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  • DOI: https://doi.org/10.1007/978-3-319-62809-7_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-62808-0

  • Online ISBN: 978-3-319-62809-7

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