Corpus ID: 119161963

Linear transformations and strong $q$-log-concavity for certain combinatorial triangle

@article{Zhu2016LinearTA,
  title={Linear transformations and strong \$q\$-log-concavity for certain combinatorial triangle},
  author={Bao-Xuan Zhu},
  journal={arXiv: Combinatorics},
  year={2016}
}
  • Bao-Xuan Zhu
  • Published 2016
  • Mathematics
  • arXiv: Combinatorics
  • It is well-known that the binomial transformation preserves the log-concavity property and log-convexity property. Let $\binom{a+n}{b+k}$ be the binomial coefficients and $\binom{n,k}{j}$ be defined by $(b_0+b_1x+\cdots+b_kx^{k})^n:=\sum_{j=0}^{kn}\binom{n,k}{j}x^j,$ where the sequence $(b_i)_{0\leq i\leq k}$ is log-concave. In this paper, we prove that the linear transformation $$y_n(q)=\sum_{k=0}^n\binom{a+n}{b+k}x_k(q)$$ preserves the strong $q$-log-concavity property for any fixed… CONTINUE READING

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