Log-balanced combinatorial sequences

Details Log-balanced combinatorial sequences Log-balanced combinatorial sequences

2006-03-16

arxiv.org/abs/math/0603403v1

International Journal of Mathematics and Mathematical Sciences 2005:4 (2005) 507-522

Mathematics

Combinatorics

24 pages, no figures

Scientific paper

10.1155/IJMMS.2005.507

We consider log-convex sequences that satisfy an additional constraint imposed on their rate of growth. We call such sequences log-balanced. It is shown that all such sequences satisfy a pair of double inequalities. Sufficient conditions for log-balancedness are given for the case when the sequence satisfies a two- (or more-) term linear recurrence. It is shown that many combinatorially interesting sequences belong to this class, and, as a consequence, that the above-mentioned double inequalities are valid for all of them.

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