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A Note on q-Stirling Numbers

Abstract

The q-Stirling numbers of both kinds are specializations of the complete or elementary symmetric functions. In this note, we use this fact to prove that the q-Stirling numbers can be expressed in terms of the q-binomial coefficients and vice versa.

Keywords

  • Elementary Symmetric Functions
  • Classical Binomial Coefficients
  • Classical Stirling Numbers
  • Schur Functions
  • Integer Partitions

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References

  1. Andrews, G.E.: The Theory of Partitions. Addison-Wesley Publishing, Reading (1976)

    MATH  Google Scholar 

  2. Call, G.S., Velleman, D.J.: Pascal’s matrices. Amer. Math. Monthly 100(4), 372–376 (1993)

    CrossRef  MATH  MathSciNet  Google Scholar 

  3. Ernst, T.: q-Stirling numbers, an umbral approach. Adv. Dyn. Syst. Appl. 3(2), 251–282 (2008)

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  4. Macdonald, I.G.: Symmetric Functions and Hall Polynomials, 2nd edn. Clarendon, Oxford (1995)

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Acknowledgements

The author expresses his gratitude to Oana Merca for the careful reading of the manuscript and helpful remarks.

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Correspondence to Mircea Merca .

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Dedicated to Professor Hari M. Srivastava

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Merca, M. (2014). A Note on q-Stirling Numbers. In: Milovanović, G., Rassias, M. (eds) Analytic Number Theory, Approximation Theory, and Special Functions. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0258-3_9

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