Set partitions with restrictions
نویسندگان
چکیده
منابع مشابه
Set partitions with circular successions
We consider the enumeration of partitions of a finite set according to the number of consecutive elements inside a block under the assumption that the elements are arranged around a circle. This statistic, commonly known as circular succession, continues to play a significant role in many combinatorial problems involving combinations of a set following its first appearance in a paper of Irving ...
متن کاملSet Partitions in R
This short paper introduces a code snippet in the form of an R function that enumerates all possible partitions of a finite set given the sizes of the equivalence classes. Three combinatorial problems are solved using the software: one from bioinformatics, one from scheduling theory, and one from forensic science.
متن کاملPartitions with Parts in a Finite Set
Abstract. For a finite set A of positive integers, we study the partition function pA(n). This function enumerates the partitions of the positive integer n into parts in A. We give simple proofs of some known and unknown identities and congruences for pA(n). For n in a special residue class, pA(n) is a polynomial in n. We examine these polynomials for linear factors, and the results are applied...
متن کاملSet partitions with successions and separations
The number of ways of partitioning a set of m elements into k nonempty subsets (called classes or blocks) is given by s2(m,k), the Stirling number of the second kind. Without loss of generality we assume that the m elements have been labeled 1,2, . . . ,m and consider k-partitions of the set [m] = {1,2, . . . ,m}. Substantial information on set partitions can be found in [3, 8]. For connections...
متن کاملRecords in Set Partitions
A partition of [n] = {1, 2, . . . , n} is a decomposition of [n] into nonempty subsets called blocks. We will make use of the canonical representation of a partition as a word over a finite alphabet, known as a restricted growth function. An element ai in such a word π is a strong (weak) record if ai > aj (ai > aj) for all j = 1, 2, . . . , i−1. Furthermore, the position of this record is i. We...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2008
ISSN: 0012-365X
DOI: 10.1016/j.disc.2007.06.041