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The
Twelvefold
Way
Title: |
The Twelvefold Way |
Author:
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Lukas Bulwahn (lukas /dot/ bulwahn /at/ gmail /dot/ com)
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Submission date: |
2016-12-29 |
Abstract: |
This entry provides all cardinality theorems of the Twelvefold Way.
The Twelvefold Way systematically classifies twelve related
combinatorial problems concerning two finite sets, which include
counting permutations, combinations, multisets, set partitions and
number partitions. This development builds upon the existing formal
developments with cardinality theorems for those structures. It
provides twelve bijections from the various structures to different
equivalence classes on finite functions, and hence, proves cardinality
formulae for these equivalence classes on finite functions. |
BibTeX: |
@article{Twelvefold_Way-AFP,
author = {Lukas Bulwahn},
title = {The Twelvefold Way},
journal = {Archive of Formal Proofs},
month = dec,
year = 2016,
note = {\url{http://isa-afp.org/entries/Twelvefold_Way.html},
Formal proof development},
ISSN = {2150-914x},
}
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License: |
BSD License |
Depends on: |
Bell_Numbers_Spivey, Card_Multisets, Card_Number_Partitions, Card_Partitions |
Status: [ok] |
This is a development version of this entry. It might change over time
and is not stable. Please refer to release versions for citations.
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