Total positivity of Toeplitz matrices of recursive hypersequences - Došlić, Tomislav (Ars mathematica contemporanea, 2019)
We present a new class of totally positive Toeplitz matrices composed of recently introduced hyperfibonacci numbers of the ?$r$?-th generation. As a consequence, we obtain that all sequences ?$F_n^{(r)}$? of hyperfibonacci numbers of ?$r$?-th generation are log-concave for ?$r \ge 1$? and large enough ?$n$?.
Keywords: Hankel matrix; Hankelova matrika; hiperfibonaccijevo zaporedje; hyperfibonacci sequence; log-concavity; log-konkavnost; Toeplitz matrix; Toeplitzova matrika; total positivity; totally positive matrix; totalna pozitivnost; totalno pozitivne matrike