Bulgarian solitaire and related operations on partitions

02/10/2009 - 12:15pm
02/10/2009 - 1:10pm
Brian Hopkins (Saint Peter's College)

Given some coins split into piles, take one from each pile to create a new pile; repeat. This is the basis of the deterministic game Bulgarian solitaire, which can be cast as an operation on partitions. Where will you end up? What partitions will you never reach? We will survey results from the initial 1982 article through recent work and open questions. Also, the operation can be generalized to a family of operations from the Bulgarian solitaire move to conjugation. The same questions can be asked for all of these operators; a nice unifying solution to one such question will be presented. Proof techniques will include generating functions and combinatorial arguments on graphical representations of partitions.

ML 211