Calculus proofs of some combinatorial inequalities
| dc.creator | Došlić, Tomislav | |
| dc.creator | Veljan, Darko | |
| dc.date | 2006-03-16 | |
| dc.date.accessioned | 2026-07-07T07:06:59Z | |
| dc.date.available | 2026-07-07T07:06:59Z | |
| dc.description | Using calculus we show how to prove some combinatorial inequalities of the type log-concavity or log-convexity. It is shown by this method that binomial coefficients and Stirling numbers of the first and second kinds are log-concave, and that Motzkin numbers and secondary structure numbers of rank 1 are log-convex. In fact, we prove via calculus a much stronger result that a natural continuous ``patchwork'' (i.e. corresponding dynamical systems) of Motzkin numbers and secondary structures recursions are increasing functions. We indicate how to prove asymptotically the log-convexity for general secondary structures. Our method also applies to show that sequences of values of some orthogonal polynomials, and in particular the sequence of central Delannoy numbers, are log-convex. | |
| dc.description | 22 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/math/0603405 | |
| dc.identifier | http://arxiv.org/abs/math/0603405 | |
| dc.identifier | Mathematical Inequalities & Applications 6 (2003) 197-209 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/110228 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A20;05A10;26A06 | |
| dc.title | Calculus proofs of some combinatorial inequalities | |
| dc.type | text |