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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Published in:Mathematische Semesterberichte 2020-10, Vol.67 (2), p.237-261
Main Authors: Carl, Merlin, Schmitz, Michael
Format: Article
Language:English
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Combinatorial analysis
Mathematics
Mathematics and Statistics
Mathematik in der Lehre
Partitions (mathematics)
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description 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.
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subjects Combinatorial analysis
Mathematics
Mathematics and Statistics
Mathematik in der Lehre
Partitions (mathematics)
title How to grow it? Strategies of mathematical development presented by the example of enumerating certain set partitions
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