Set Partitions in R
نویسندگان
چکیده
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.
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 کاملCrossings and Nestings in Colored Set Partitions
Chen, Deng, Du, Stanley, and Yan introduced the notion of k-crossings and k-nestings for set partitions, and proved that the sizes of the largest k-crossings and k-nestings in the partitions of an n-set possess a symmetric joint distribution. This work considers a generalization of these results to set partitions whose arcs are labeled by an r-element set (which we call r-colored set partitions...
متن کاملA local approach to the entropy of countable fuzzy partitions
This paper denes and investigates the ergodic proper-ties of the entropy of a countable partition of a fuzzy dynamical sys-tem at different points of the state space. It ultimately introducesthe local fuzzy entropy of a fuzzy dynamical system and proves itto be an isomorphism invariant.
متن کاملTsallis 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 کاملChains in the lattice of noncrossing partitions
The lattice of noncrossing set partitions is known to admit an R-labeling. Under this labeling, maximal chains give rise to permutations. We discuss structural and enumerative properties of the lattice of noncrossing partitions, which pertain to a new permutation statistic, m(a), defined as the number of maximal chains labeled by 0. Miibius inversion results and related facts about the lattice ...
متن کامل