منابع مشابه
On Carlitz Compositions
This paper deals with Carlitz compositions of natural numbers (adjacent parts have to be different). The following parameters are analysed: number of parts, number of equal adjacent parts in ordinary compositions, largest part, Carlitz compositions with zeros allowed (correcting an erroneous formula from Carlitz). It is also briefly demonstrated that so-called 1-compositions of a natural number...
متن کاملGeneralizations of Carlitz Compositions
We consider a class of generating functions that appear in the context of Carlitz compositions. In order to combinatorially interpret them, we introduce a combinatorial structures that we name generalized compositions and p-Carlitz compositions of integers. We explain their connection to Carlitz compositions, the relation to other combinatorial structures, and we describe their basic properties...
متن کاملProbabilistic Analysis of Carlitz Compositions
Using generating functions and limit theorems, we obtain a stochastic description of Carlitz compositions of large integer n (i.e. compositions two successive parts of which are different). We analyze: the number M of parts, the number of compositions T (m,n) with m parts, the distribution of the last part size, the correlation between two successive parts, leading to a Markov chain. We describ...
متن کاملSome Stochastic Properties of Random Classical and Carlitz Compositions
Some Stochastic Properties of Random Classical and Carlitz Compositions Boris Leonid Kheyfets Pawel Hitczenko, Ph.D. Several stochastic parameters of random classical and Carlitz (adjacent parts are different) compositions of integer n are considered. An exact formula is obtained for the average multiplicity and the variance of the multiplicity of a given part size in the classical case. Furthe...
متن کاملCarlitz Extensions
The ring Z has many analogies with the ring Fp[T ], where Fp is a field of prime size p. For example, for nonzero m ∈ Z and nonzero M ∈ Fp[T ], the residue rings Z/(m) and Fp[T ]/M are both finite. The unit groups Z × = {±1} and Fp[T ]× = Fp are both finite. Every nonzero integer can be made positive after multiplication by a suitable unit, and every nonzero polynomial in Fp[T ] can be made mon...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 1998
ISSN: 0195-6698
DOI: 10.1006/eujc.1998.0216