Some Summation Formulae over the Set of Partitions 97

نویسنده

  • W. C. CHU
چکیده

Some algebraic identities with independent variables are established by means of the calculus on formal power series. Applications to special functions and classical polynomials are also demonstrated.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Some Summation Formulae over the Set of Partitions

Let σ(n) denote the set of partitions of n (a nonnegative integer) usually denoted by 1122 . . . nn with ∑ iki = n; ki is, of course, the number of partitions of size i. If the number of parts for the partition set of n is restricted to k, i.e., ∑ ki = k; then the corresponding subset of σ(n) is denoted by σ(n, k). For nonnegative integral vector k̄ = (k1, . . . , kn), the multinomial coefficien...

متن کامل

k-Efficient partitions of graphs

A set $S = {u_1,u_2, ldots, u_t}$ of vertices of $G$ is an efficientdominating set if every vertex of $G$ is dominated exactly once by thevertices of $S$. Letting $U_i$ denote the set of vertices dominated by $u_i$%, we note that ${U_1, U_2, ldots U_t}$ is a partition of the vertex setof $G$ and that each $U_i$ contains the vertex $u_i$ and all the vertices atdistance~1 from it in $G$. In this ...

متن کامل

Stirling number of the fourth kind and lucky partitions of a finite set

The concept of Lucky k-polynomials and in particular Lucky χ-polynomials was recently introduced. This paper introduces Stirling number of the fourth kind and Lucky partitions of a finite set in order to determine either the Lucky k- or Lucky χ-polynomial of a graph. The integer partitions influence Stirling partitions of the second kind.

متن کامل

Explicit formulae for Kerov polynomials

We prove two formulae expressing the Kerov polynomial Σk as a weighted sum over the set of noncrossing partitions of the set {1, . . . , k + 1}. We also give a combinatorial description of a family of symmetric functions specializing in the coefficients of Σk .

متن کامل

Tsallis Entropy and Conditional Tsallis Entropy of Fuzzy Partitions

The purpose of this study is to define the concepts of Tsallis entropy and conditional Tsallis entropy of fuzzy partitions and to obtain some results concerning this kind entropy. We show that the Tsallis entropy of fuzzy partitions has the subadditivity and concavity properties. We study this information measure under the refinement and zero mode subset relations. We check the chain rules for ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007