Ordinal sums, clockwise hackenbush, and domino shave
Main Author: | |
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Publication Date: | 2020 |
Other Authors: | , , |
Format: | Article |
Language: | eng |
Source: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Download full: | http://hdl.handle.net/10400.21/14829 |
Summary: | We present two rulesets, domino shave and clockwise hackenbush . The first is somehow natural and, as special cases, includes stirling shave and Hetyei’s Bernoulli game. Clockwise hackenbush seems artificial yet it is equivalent to domino shave. From the pictorial form of the game, and a knowledge of hackenbush, the decomposition into ordinal sums is immediate. The values of clockwise blue-red hackenbush are numbers and we provide an explicit formula for the ordinal sum of numbers where the literal form of the base is { x | } or { | x }, and x is a number. That formula generalizes van Roode’s signed binary number method for blue-red hackenbush. |
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Ordinal sums, clockwise hackenbush, and domino shaveCombinatorial game theoryHackenbushvan Roode’s methodOrdinal sumWe present two rulesets, domino shave and clockwise hackenbush . The first is somehow natural and, as special cases, includes stirling shave and Hetyei’s Bernoulli game. Clockwise hackenbush seems artificial yet it is equivalent to domino shave. From the pictorial form of the game, and a knowledge of hackenbush, the decomposition into ordinal sums is immediate. The values of clockwise blue-red hackenbush are numbers and we provide an explicit formula for the ordinal sum of numbers where the literal form of the base is { x | } or { | x }, and x is a number. That formula generalizes van Roode’s signed binary number method for blue-red hackenbush.RCIPLCarvalho, AldaHuggan, Melissa A.Nowakowski, RichardSantos, Carlos2022-07-13T10:58:27Z2020-11-242020-11-24T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.21/14829engCARVALHO, Alda; [et al] – Ordinal sums, clockwise hackenbush, and domino shave. Integers. Electronic Journal of Combinatorial Number Theory. Vol. 21B (2021), pp. 1-23.info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-08-03T10:11:31Zoai:repositorio.ipl.pt:10400.21/14829Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:22:33.848329Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Ordinal sums, clockwise hackenbush, and domino shave |
title |
Ordinal sums, clockwise hackenbush, and domino shave |
spellingShingle |
Ordinal sums, clockwise hackenbush, and domino shave Carvalho, Alda Combinatorial game theory Hackenbush van Roode’s method Ordinal sum |
title_short |
Ordinal sums, clockwise hackenbush, and domino shave |
title_full |
Ordinal sums, clockwise hackenbush, and domino shave |
title_fullStr |
Ordinal sums, clockwise hackenbush, and domino shave |
title_full_unstemmed |
Ordinal sums, clockwise hackenbush, and domino shave |
title_sort |
Ordinal sums, clockwise hackenbush, and domino shave |
author |
Carvalho, Alda |
author_facet |
Carvalho, Alda Huggan, Melissa A. Nowakowski, Richard Santos, Carlos |
author_role |
author |
author2 |
Huggan, Melissa A. Nowakowski, Richard Santos, Carlos |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
RCIPL |
dc.contributor.author.fl_str_mv |
Carvalho, Alda Huggan, Melissa A. Nowakowski, Richard Santos, Carlos |
dc.subject.por.fl_str_mv |
Combinatorial game theory Hackenbush van Roode’s method Ordinal sum |
topic |
Combinatorial game theory Hackenbush van Roode’s method Ordinal sum |
description |
We present two rulesets, domino shave and clockwise hackenbush . The first is somehow natural and, as special cases, includes stirling shave and Hetyei’s Bernoulli game. Clockwise hackenbush seems artificial yet it is equivalent to domino shave. From the pictorial form of the game, and a knowledge of hackenbush, the decomposition into ordinal sums is immediate. The values of clockwise blue-red hackenbush are numbers and we provide an explicit formula for the ordinal sum of numbers where the literal form of the base is { x | } or { | x }, and x is a number. That formula generalizes van Roode’s signed binary number method for blue-red hackenbush. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-11-24 2020-11-24T00:00:00Z 2022-07-13T10:58:27Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10400.21/14829 |
url |
http://hdl.handle.net/10400.21/14829 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
CARVALHO, Alda; [et al] – Ordinal sums, clockwise hackenbush, and domino shave. Integers. Electronic Journal of Combinatorial Number Theory. Vol. 21B (2021), pp. 1-23. |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799133497597624320 |