Journal of Integer Sequences, Vol. 29 (2026), Article 26.2.5

Total Positivity of Toeplitz Matrices Involving Generalized Hyper-Fibonacci Numbers


Abdelhak Taane
University of Kasdi Merbah
Department of Mathematics
Laboratory of Applied Mathematics
Ouargla, 30000
Algeria

Ihab-Eddine Djellas
CERIST Scientific and Technical Information Research Center
Algiers
Algeria
and
University of Sciences and Technology Houari Boumediene (USTHB)
Faculty of Mathematics
RECITS Laboratory
P. O. Box 32, El Alia, 16111
Bab Ezzouar, Algiers
Algeria

Mohammed Mekkaoui
École Normale Supérieure
Department of Mathematics
EDPNLHM Laboratory
B. P. 92, Vieux Kouba, 16050
Kouba, Algiers
Algeria

Abstract:

We study the total positivity of Toeplitz matrices built from generalized hyper- Fibonacci sequences of a fixed generation. Using this approach, we prove that each sequence becomes log-concave beyond a certain point for every generation. We also present several notable special cases that illustrate the scope of our results.

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(Concerned with sequences A000032 A000045 A000129 A001333.)

Received May 12 2025; revised versions received May 14 2025; February 26 2026. Published in Journal of Integer Sequences, April 22 2026.

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