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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Garden of Eden States in Austrian Solitaire

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Author(s):
da Silva, Robson [1] ; Hopkins, Brian [2] ; Sellers, James A. [3]
Total Authors: 3
Affiliation:
[1] Univ Fed Sao Paulo, BR-12247 Sao Jose Dos Campos, SP - Brazil
[2] St Peters Univ, Jersey City, NJ 07306 - USA
[3] Univ Minnesota, Duluth, MN 55812 - USA
Total Affiliations: 3
Document type: Journal article
Source: EUROPEAN JOURNAL OF COMBINATORICS; v. 83, JAN 2020.
Web of Science Citations: 0
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. (C) 2019 Elsevier Ltd. All rights reserved. (AU)

FAPESP's process: 16/14057-2 - Additive number theory in the integers and in function fields
Grantee:Robson Oliveira da Silva
Support Opportunities: Scholarships abroad - Research