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Ordinal sums, clockwise hackenbush, and domino shave

2020-11-24Journal article Open access
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dc.contributor.authorCarvalho, Alda
dc.contributor.authorHuggan, Melissa A.
dc.contributor.authorNowakowski, Richard
dc.contributor.authorSantos, Carlos
dc.date.accessioned2022-07-13T10:58:27Z
dc.date.available2022-07-13T10:58:27Z
dc.date.issued2020-11-24
dc.description.abstractWe 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.pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.citationCARVALHO, Alda; [et al] – Ordinal sums, clockwise hackenbush, and domino shave. Integers. Electronic Journal of Combinatorial Number Theory. Vol. 21B (2021), pp. 1-23.pt_PT
dc.identifier.urihttp://hdl.handle.net/10400.21/14829
dc.language.isoengpt_PT
dc.relationPDF-532564-2019 - Natural Sciences and Engineering Research Council of Canadapt_PT
dc.relationCEMAPRE - Centre for Applied Mathematics and Economics
dc.relationCenter for Functional Analysis, Linear Structures and Applications
dc.subjectCombinatorial game theorypt_PT
dc.subjectHackenbushpt_PT
dc.subjectvan Roode’s methodpt_PT
dc.subjectOrdinal sumpt_PT
dc.titleOrdinal sums, clockwise hackenbush, and domino shavept_PT
dc.typejournal article
dspace.entity.typePublication
oaire.awardTitleCEMAPRE - Centre for Applied Mathematics and Economics
oaire.awardTitleCenter for Functional Analysis, Linear Structures and Applications
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UID%2FMulti%2F00491%2F2019/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UID%2FMAT%2F04721%2F2019/PT
oaire.citation.endPage23pt_PT
oaire.citation.startPage1pt_PT
oaire.citation.titleIntegers. Electronic Journal of Combinatorial Number Theorypt_PT
oaire.citation.volume21Bpt_PT
oaire.fundingStream6817 - DCRRNI ID
oaire.fundingStream6817 - DCRRNI ID
person.familyNameCarvalho
person.familyNameNowakowski
person.familyNameSantos
person.givenNameAlda
person.givenNameRichard
person.givenNameCarlos
person.identifierR-000-PGY
person.identifier.ciencia-idFD18-CBDD-B7C7
person.identifier.ciencia-idA210-4691-62EE
person.identifier.orcid0000-0003-2642-4947
person.identifier.orcid0000-0002-4434-672X
person.identifier.orcid0000-0001-6609-6541
person.identifier.ridP-1444-2015
person.identifier.scopus-author-id25027091800
person.identifier.scopus-author-id7005512531
person.identifier.scopus-author-id36961140800
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.rightsopenAccesspt_PT
rcaap.typearticlept_PT
relation.isAuthorOfPublication214fa21c-bca0-4769-99b0-5f1239d2ea41
relation.isAuthorOfPublication52e9a141-27bb-4460-ae37-caf8dba61b95
relation.isAuthorOfPublicationc9e068b1-f2c6-40fd-bc55-82d15b822822
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