Naslov
Log-convexity of combinatorial sequences from their convexity

Autori
Došlić, Tomislav

Izvornik
Journal of Mathematical Inequalities (1846-579X) 3 (2009), 3; 437-442

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
log-convexity; convexity; combinatorial sequences; Motzkin numbers

Sažetak
A sequence $(x_n)_{; ; ; ; ; n \geq 0}; ; ; ; ; $ of positive real numbers is log-convex if the inequality $x_n^2 \leq x_{; ; ; ; ; n-1}; ; ; ; ; x_{; ; ; ; ; n+1}; ; ; ; ; $ is valid for all $n \geq 1$. We show here how the problem of establishing the log-convexity of a given combinatorial sequence can be reduced to examining the ordinary convexity of related sequences. The new method is then used to prove that the sequence of Motzkin numbers is log-convex.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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