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Log-concave sequences of bi $$^s$$ s nomial coefficients with their analogs and symmetric functions

Author

Listed:
  • Abdelghafour Bazeniar

    (university of Mohamed Seddik Benyahia
    University center of Abdelhafid Boussouf)

  • Moussa Ahmia

    (university of Mohamed Seddik Benyahia)

  • Abderrahmane Bouchair

    (university of Mohamed Seddik Benyahia)

Abstract

In this paper, we prove the strong log-concavity and the unimodality of the various sequences of an extension of elementary symmetric function. The principal technique used is a combinatorial interpretation of determinants using lattice paths due to Gessel and Viennot. As applications, we establish the strong q-log-concavity and the unimodality of q-bi $$^{s}$$ s nomial coefficients and their sequences lying on rays of the associated triangle.

Suggested Citation

  • Abdelghafour Bazeniar & Moussa Ahmia & Abderrahmane Bouchair, 2022. "Log-concave sequences of bi $$^s$$ s nomial coefficients with their analogs and symmetric functions," Indian Journal of Pure and Applied Mathematics, Springer, vol. 53(1), pages 127-137, March.
    • Handle: RePEc:spr:indpam:v:53:y:2022:i:1:d:10.1007_s13226-021-00018-7
    DOI: 10.1007/s13226-021-00018-7
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