Journal of Integer Sequences, Vol. 23 (2020), Article 20.5.3

Log-Concavity and LC-Positivity for Generalized Triangles

Moussa Ahmia
Laboratoires Mathématiques et Applications des Mathématiques
Department of Mathematics
Université Mohammed Seddik BenYahia
Jijel 18000

Hacène Belbachir
RECITS Laboratory
Faculty of Mathematics
University of Science and Technology Houari Boumediene
BP 32
El Alia 16111
Bab Ezzouar


In this paper, we propose the generalized triangles called s-triangles for s a given positive integer, as a bi-indexed sequence of nonnegative numbers {as(n, k)}0 ≤ kns satisfying as(n, k) = 0 for k < 0. We extend some results of Wang and Yeh, and show that if the s-triangle is LC-positive (resp., doubly LC-positive) then it preserves (resp., it doubly preserves) the log-concavity of the sequences. Applications related to bisnomial coefficients are given.

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(Concerned with sequences A000045 A008287 A027907 A035343.)

Received May 30 2019; revised versions received January 2 2020; January 3 2020. Published in Journal of Integer Sequences, May 11 2020.

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