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
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
{as(n, k)}0 ≤ k ≤
ns 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.
Full version: pdf,
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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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