[seqfan] "Stable" Partitions

[Ali Sada]

Hi Everyone,

I am not familiar with the literature of partitions, and I would really appreciate it if you could show me the OEIS sequences that are associated with the idea below.


k is a part of partition of a positive integer n. k has k number of “bonds” that connects it to the other parts of the partition. For a partition to be “stable” all the bonds of its parts must be fulfilled.

Some partitions form a cycle or cycles. For example, 8 has 2 cycles. The first one is four 2’s each one connected the other by one bond. The second one is two 3’s each connected to each other by two bonds, and each connected to 2 by one bond. 

The sequences associated with this idea could be: Number of stable forms of partitions of 2n, number of distinct "molecules", number of cycles, etc.

Best,
 

Ali