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

Abdelghafour Bazeniar (), Moussa Ahmia () and Abderrahmane Bouchair ()
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Abdelghafour Bazeniar: university of Mohamed Seddik Benyahia
Moussa Ahmia: university of Mohamed Seddik Benyahia
Abderrahmane Bouchair: university of Mohamed Seddik Benyahia

Indian Journal of Pure and Applied Mathematics, 2022, vol. 53, issue 1, 127-137

Abstract: 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.

Keywords: Log-concavity; unimodality; bi $$^{s}$$ s nomial; symmetric functions; lattice paths.; 05A10; 05A20; 05A30; 05E05; 11B65. (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13226-021-00018-7

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