A partition of $[n]$ is indecomposable if no subset of its blocks partitions $[k]$ with $k \in [n-1]$. Irreducible set partitions are defined at <http://oeis.org/A055105> . Both are counted by <http://oeis.org/A074664> . Is any bijection between them known?



Is there a bijection from indecomposable to irreducible set partitions?
Mike Zabrocki has kindly addressed me to the following note <http://www.billchen.org/publications/2011_P7_Unsplitable/2011_P7_Unsplitable.pdf> where the bijection is built (here "atomic"="indecomposable" and "unsplittable"="irreducible"). Note that the correct version of the definition of splittable or reducible partition (page 3 on top) allows different lengths for the reducing partitions (a small but important detail that will be fixed in the OEIS link).


