partitietabellen

Partitietabellen, in Dutch mathematical and scientific literature, refer to tabular presentations that summarize partitions. The term is used for tables that organize and display partition-related data and can refer to different but related concepts in combinatorics and number theory.

One common use is partitions of a finite set. A partition of an n-element set divides the set into nonempty, disjoint blocks whose union is the whole set. The number of partitions into k blocks is given by the Stirling numbers of the second kind S(n, k), and the total number of partitions is the Bell number B_n. A partitietabel in this context may present the values S(n, k) for ranges of n and k, forming a triangular array that encodes how partitions into different numbers of blocks occur.

Another frequent use concerns partitions of integers. An integer partition of n is a way of writing n as a sum of positive integers, where order is not important. The total number of partitions is denoted p(n). Partitietabellen for integer partitions often list p(n) for successive n and may be refined to show partitions by number of parts or by largest part. Such tables are connected to generating functions, recurrences, and various structural representations like Ferrers or Young diagrams, which accompany the tabular data in many expositions.

Partitietabellen serve as reference data in combinatorics, number theory, and related fields, helping to illustrate properties of partitions and to support both teaching and research. The exact form of a partition table can vary by context, reflecting whether it concerns set partitions, integer partitions, or related combinatorial statistics.