How to grow it? Strategies of mathematical development presented by the example of enumerating certain set partitions

We describe in the form of a dialogue a development of various reflections on the combinatorics of set partitions; among the topics we pursue are the number of ways of partitioning a finite set into a fixed number d of subsets of odd or even size, into a parts of odd and b parts of even size, and in...

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Bibliographic Details
Published in:Mathematische Semesterberichte 2020-10, Vol.67 (2), p.237-261
Main Authors: Carl, Merlin, Schmitz, Michael
Format: Article
Language:English
Subjects:
Combinatorial analysis
Mathematics
Mathematics and Statistics
Mathematik in der Lehre
Partitions (mathematics)
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Summary:We describe in the form of a dialogue a development of various reflections on the combinatorics of set partitions; among the topics we pursue are the number of ways of partitioning a finite set into a fixed number d of subsets of odd or even size, into a parts of odd and b parts of even size, and into d parts, each of which has a size in a certain congruence class modulo some natural number m . To this end, pattern guessing, recursion and induction, combinatorial interpretation and generating functions are employed. The participants of the dialogue represent different perspectives on and approaches to mathematics.
ISSN:0720-728X
1432-1815
DOI:10.1007/s00591-019-00267-y