The Asymptotic Number of Set Partitions with Unequal Block Sizes
نویسندگان
چکیده
The asymptotic behavior of the number of set partitions of an n-element set into blocks of distinct sizes is determined. This behavior is more complicated than is typical for set partition problems. Although there is a simple generating function, the usual analytic methods for estimating coefficients fail in the direct approach, and elementary approaches combined with some analytic methods are used to obtain most of the results. Simultaneously, we obtain results on the shape of a random partition of an n-element set into blocks of distinct sizes. Mathematics Subject Classification (1991): 05A18, 05A16
منابع مشابه
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 کاملk-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 کاملOptimum Block Size in Separate Block Bootstrap to Estimate the Variance of Sample Mean for Lattice Data
The statistical analysis of spatial data is usually done under Gaussian assumption for the underlying random field model. When this assumption is not satisfied, block bootstrap methods can be used to analyze spatial data. One of the crucial problems in this setting is specifying the block sizes. In this paper, we present asymptotic optimal block size for separate block bootstrap to estimate the...
متن کاملAnalysis of Some New Partition Statistics
The study of partition statistics can be said to have begun with Erdős and Lehner [3] in 1941, who studied questions concerning the normal, resp. average value over all partitions of n of quantities such as the number of parts, the number of different part sizes, and the size of the largest part. To begin with, instead of looking at parts in partitions we will look at gaps, that is, at part siz...
متن کاملPartitions with Fixed Number of Sizes
Let t(n, s) and t(n, k, s), respectively, be the number of partitions of n with s different sizes, and the number of partitions of n with exactly k parts and s different sizes. In this article, an asymptotic estimate for t(n, k, s) is presented for the following two cases: (i) s = k − 1 and (ii) when k is a prime number with s = 2. Further, the enumeration of uniform partitions with exactly 2 s...
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:
- Electr. J. Comb.
دوره 6 شماره
صفحات -
تاریخ انتشار 1999