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Log-Concavity and LC-Positivity for Generalized Triangles
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Moussa Ahmia

Laboratoires Mathématiques et Applications des Mathématiques

Department of Mathematics

Université Mohammed Seddik BenYahia

Jijel 18000

Algeria

Hacène Belbachir

RECITS Laboratory

Faculty of Mathematics

University of Science and Technology Houari Boumediene

BP 32

El Alia 16111

Bab Ezzouar

Algiers

Algeria

**Abstract:**

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
{*a*_{s}(*n*, *k*)}_{0 ≤ k ≤
ns} satisfying *a*_{s}(*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 bi^{s}nomial 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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