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

Autor: Michael Schmitz, Merlin Carl
Rok vydání: 2019
Předmět:
Zdroj: Mathematische Semesterberichte. 67:237-261
ISSN: 1432-1815
0720-728X
DOI: 10.1007/s00591-019-00267-y
Popis: 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.
Databáze: OpenAIRE
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