Garden of Eden States in Austrian Solitaire

Robson da Silva, Brian Hopkins, James A. Sellers

Research output: Contribution to journalArticle


Introduced by Akin and Davis in 1985, Austrian Solitaire is a two-parameter variation of the better known Bulgarian Solitaire that constrains part sizes. We count the valid states in Austrian Solitaire and also the number of states with no preimage, known as Garden of Eden states. Connecting these two quantities involves new results about preimages in the system. Our tools for this work include bijective proofs and generating functions.

Original languageEnglish (US)
Article number103023
JournalEuropean Journal of Combinatorics
StatePublished - Jan 2020


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