Abstract
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 language | English (US) |
|---|---|
| Article number | 103023 |
| Journal | European Journal of Combinatorics |
| Volume | 83 |
| DOIs | |
| State | Published - Jan 2020 |
Bibliographical note
Funding Information:The first named author was supported by the São Paulo Research Foundation, FAPESP grant no. 2016/14057-2 . The tables and equivalent versions of Propositions 2.1 and 3.1 appeared in the 2012 undergraduate honors thesis of Kapil Bastola [3] , whose Conjecture 1 is resolved by Theorem 3.2 ; the second named author served as faculty advisor. The authors are grateful for George Andrews’s assistance in simplifying the generating function given in Theorem 3.2 . We also appreciate the careful reading and thoughtful recommendations of two anonymous reviewers.
Funding Information:
The first named author was supported by the S?o Paulo Research Foundation, FAPESP grant no. 2016/14057-2. The tables and equivalent versions of Propositions 2.1 and 3.1 appeared in the 2012 undergraduate honors thesis of Kapil Bastola [3], whose Conjecture 1 is resolved by Theorem 3.2; the second named author served as faculty advisor. The authors are grateful for George Andrews's assistance in simplifying the generating function given in Theorem 3.2. We also appreciate the careful reading and thoughtful recommendations of two anonymous reviewers.
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