The Twelvefold Way

Lukas Bulwahn 📧

December 29, 2016

This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.


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.


BSD License


Session Twelvefold_Way