منابع مشابه
On composition of generating functions
In this work we study numbers and polynomials generated by two type of composition of generating functions and get their explicit formulae. Furthermore we state an improvementof the composita formulae's given in [6] and [3], using the new composita formula's we construct a variety of combinatorics identities. This study go alone to dene new family of generalized Bernoulli polynomials which incl...
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We find an explicit expression of the Tutte polynomial of an $n$-fan. We also find a formula of the Tutte polynomial of an $n$-wheel in terms of the Tutte polynomial of $n$-fans. Finally, we give an alternative expression of the Tutte polynomial of an $n$-wheel and then prove the explicit formula for the Tutte polynomial of an $n$-wheel.
متن کاملProbability Generating Functions for Sattolo’s Algorithm
In 1986 S. Sattolo introduced a simple algorithm for uniform random generation of cyclic permutations on a fixed number of symbols. Recently, H. Prodinger analysed two important random variables associated with the algorithm, and found their mean and variance. H. Mahmoud extended Prodinger’s analysis by finding limit laws for the same two random variables.The present article, starting from the ...
متن کاملGenerating functions for generating trees
Certain families of combinatorial objects admit recursive descriptions in terms of generating trees: each node of the tree corresponds to an object, and the branch leading to the node encodes the choices made in the construction of the object. Generating trees lead to a fast computation of enumeration sequences (sometimes, to explicit formulae as well) and provide efficient random generation al...
متن کاملGenerating Functions
gives a single object representing the entire sequence. This is particularly useful when the series is the Taylor series of a familiar function. An important example is ak D 1 for all k 0. The series A.x/ is a geometric series that is known to converge to .1 x/ . Other examples are obtained by performing simple operations on this one. When you met infinite series in Calculus, the Taylor series ...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 1975
ISSN: 0090-5364
DOI: 10.1214/aos/1176343291