Level Sizes of the Bulgarian Solitaire Game Tree
(English)In: The Fibonacci quarterly, ISSN 0015-0517, ISSN 0015-0517Article in journal (Refereed) Accepted
Bulgarian solitaire is a dynamical system on integer partitions of n which converges to a unique fixed point if n=1+2+...+k is a triangular number. There are few results about the structure of the game tree, but when k tends to infinity the game tree itself converges to astructure that we are able to analyze. Its level sizes turns out to be a bisection of the Fibonacci numbers. The leaves in this tree structure are enumerated using Fibonacci numbers as well.We also demonstrate to which extent these results apply to the case when k is finite.
Place, publisher, year, edition, pages
The Fibonacci Association.
Research subject Mathematics/Applied Mathematics
IdentifiersURN: urn:nbn:se:mdh:diva-35012OAI: oai:DiVA.org:mdh-35012DiVA: diva2:1081111
FunderSwedish Research Council, 2010-5565