On the Total Positivity of Delannoy-Like Triangles

نویسندگان

  • Lili Mu
  • Sai-nan Zheng
چکیده

where e, h are both nonnegative and dn,k = 0 unless n ≥ k ≥ 0. We call D(e, h) the Delannoy-like triangle. The entries dn,k count lattice paths from (0, 0) to (n − k, k) using the steps (0, 1), (1, 0) and (1, 1) with assigned weights 1, e, and h. Some wellknown combinatorial triangles are such matrices, including the Pascal triangle D(1, 0), the Fibonacci triangle D(0, 1), and the Delannoy triangle D(1, 1). Futhermore, the Schröder triangle and Catalan triangle also arise as inverses of Delannoy-like triangles. Here we investigate the total positivity of Delannoy-like triangles. In addition, we show that each row and diagonal of Delannoy-like triangles are all PF sequences.

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تاریخ انتشار 2016