Abstract:

Whenever you come across piles of objects, take one from each pile to create a new pile. Repeat, and you are playing Bulgarian solitaire, so named by Henrik Eriksson and made famous by Martin Gardner in 1982.

Iterating this operation on partitions, when and where will you end up? What partitions will you never reach? We will review recent work and open questions. Also, the operation generalizes to a family of operations with conjugation at the other extreme. The same questions can be asked for all of these operators and one of them has a nice unifying answer.

The arguments are mostly graphical but be prepared for a generating function.