Logarithmic behavior of some combinatorial sequences
نویسندگان
چکیده
Two general methods for establishing the logarithmic behavior of recursively defined sequences of real numbers are presented. One is the interlacing method, and the other one is based on calculus. Both methods are used to prove logarithmic behavior of some combinatorially relevant sequences, such as Motzkin and Schröder numbers, sequences of values of some classic orthogonal polynomials, and many others. The calculus method extends also to two(or more) indexed sequences.
منابع مشابه
Strong convergence on weakly logarithmic combinatorial assemblies
We deal with the random combinatorial structures called assemblies. By weakening the logarithmic condition which assures regularity of the number of components of a given order, we extend the notion of logarithmic assemblies. Using the author’s analytic approach, we generalize the so-called Fundamental Lemma giving independent process approximation in the total variation distance of the compone...
متن کاملOn the Properties of Balancing and Lucas-Balancing $p$-Numbers
The main goal of this paper is to develop a new generalization of balancing and Lucas-balancing sequences namely balancing and Lucas-balancing $p$-numbers and derive several identities related to them. Some combinatorial forms of these numbers are also presented.
متن کاملThermal anomalies detection before earthquake using three filters (Fourier, Wavelet and Logarithmic Differential Filter), A Case Study of two Earthquakes in Iran
Earthquake is one of the most destructive natural phenomena which has human and financial losses. The existence of an efficient prediction system and early warning system will be useful for reducing effects of destroying earthquake. In this research, the soil temperature time-series data, obtained from three meteorological station, using three filters (Fourier, Wavelet and Logarithmic Different...
متن کاملGeneral combinatorial schemas : 159 Gaussian limit distributions and exponential tails *
1 Flajolet, P. and M. Soria, General combinatorial schemas: Gaussian limit distributions and exponential tails, Discrete Mathematics 114 (1993) 159-180. Under general conditions, the number of components in combinatorial structures defined as sequences, cycles or sets of components admits a Gaussian limit distribution together with an exponential tail. The results are valid, assuming simple ana...
متن کاملSome Algebraic and Combinatorial Properties of the Complete $T$-Partite Graphs
In this paper, we characterize the shellable complete $t$-partite graphs. We also show for these types of graphs the concepts vertex decomposable, shellable and sequentially Cohen-Macaulay are equivalent. Furthermore, we give a combinatorial condition for the Cohen-Macaulay complete $t$-partite graphs.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Discrete Mathematics
دوره 308 شماره
صفحات -
تاریخ انتشار 2008