Garden of Eden States in Austrian Solitaire

Robson da Silva; Brian Hopkins; James A. Sellers

doi:10.1016/j.ejc.2019.103023

Garden of Eden States in Austrian Solitaire

Robson da Silva, Brian Hopkins, James A. Sellers

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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	https://doi.org/10.1016/j.ejc.2019.103023
State	Published - Jan 2020

Bibliographical note

Publisher Copyright:
© 2019 Elsevier Ltd

Publisher link

10.1016/j.ejc.2019.103023

Find It

Find It at U of M Libraries

Cite this

@article{f9e9c926e5c144ef9c0544009fff24ab,

title = "Garden of Eden States in Austrian Solitaire",

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.",

author = "{da Silva}, Robson and Brian Hopkins and Sellers, {James A.}",

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier Ltd",

year = "2020",

month = jan,

doi = "10.1016/j.ejc.2019.103023",

language = "English (US)",

volume = "83",

journal = "European Journal of Combinatorics",

issn = "0195-6698",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Garden of Eden States in Austrian Solitaire

AU - da Silva, Robson

AU - Hopkins, Brian

AU - Sellers, James A.

PY - 2020/1

Y1 - 2020/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85072551962&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85072551962&partnerID=8YFLogxK

U2 - 10.1016/j.ejc.2019.103023

DO - 10.1016/j.ejc.2019.103023

M3 - Article

AN - SCOPUS:85072551962

SN - 0195-6698

VL - 83

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

M1 - 103023

ER -

Garden of Eden States in Austrian Solitaire

Abstract

Bibliographical note

Publisher link

Find It

Other files and links

Fingerprint

Cite this