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Ordinal sums of impartial games

2018-07-10Journal article Restricted access
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dc.contributor.authorCarvalho, Alda
dc.contributor.authorNeto, João
dc.contributor.authorSantos, Carlos
dc.date.accessioned2018-11-29T11:49:21Z
dc.date.available2018-11-29T11:49:21Z
dc.date.issued2018-07-10
dc.description.abstractIn an ordinal sum of two combinatorial games G and H, denoted by G : H, a player may move in either G (base) or H (subordinate), with the additional constraint that any move on G completely annihilates the component H. It is well-known that the ordinal sum does not depend on the form of its subordinate, but depends on the form of its base. In this work, we analyze g(G : H) where G and H are impartial forms, observing that the g-values are related to the concept of minimum excluded value of order k. As a case study, we introduce the ruleset OAK, a generalization of GREEN HACKENBUSH. By defining the operation gin sum, it is possible to determine the literal forms of the bases in polynomial time. (C) 2017 Elsevier B.V. All rights reserved.pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.citationCARVALHO, Alda; NETO, João Pedro; SANTOS, Carlos – Ordinal sums of impartial games. Discrete Applied Mathematics. ISSN 0166-218X. Vol. 243 (2018), pp. 39-45pt_PT
dc.identifier.doihttps://doi.org/10.1016/j.dam.2017.12.020pt_PT
dc.identifier.issn0166-218X
dc.identifier.issn1872-6771
dc.identifier.urihttp://hdl.handle.net/10400.21/9108
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherElsevierpt_PT
dc.relation.publisherversionhttps://reader.elsevier.com/reader/sd/pii/S0166218X17306005?token=B03666B01237AAF2EDC704C1328806FCD96E3B993D5AEF32A7B7EFE10430C845638FFA05EDE435023D362204788E6F0Bpt_PT
dc.subjectCombinatorial game theorypt_PT
dc.subjectGin sumpt_PT
dc.subjectImpartial gamespt_PT
dc.subjectMinimum excluded valuept_PT
dc.subjectNormal-playpt_PT
dc.subjectOAKpt_PT
dc.subjectOrdinal sumpt_PT
dc.titleOrdinal sums of impartial gamespt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/5876/UID%2FMulti%2F00491%2F2013/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/5876/UID%2FMAT%2F04721%2F2013/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/5876/UID%2FMulti%2F04046%2F2013/PT
oaire.citation.endPage45pt_PT
oaire.citation.startPage39pt_PT
oaire.citation.titleDiscrete Applied Mathematicspt_PT
oaire.citation.volume243pt_PT
oaire.fundingStream5876
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oaire.fundingStream5876
person.familyNameCarvalho
person.familyNameNeto
person.familyNameSantos
person.givenNameAlda
person.givenNameJoão
person.givenNameCarlos
person.identifierR-000-PGY
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person.identifier.ciencia-id5510-BEF8-0112
person.identifier.ciencia-idA210-4691-62EE
person.identifier.orcid0000-0003-2642-4947
person.identifier.orcid0000-0002-3974-0685
person.identifier.orcid0000-0001-6609-6541
person.identifier.ridM-1790-2015
person.identifier.ridP-1444-2015
person.identifier.scopus-author-id25027091800
person.identifier.scopus-author-id35609215700
person.identifier.scopus-author-id36961140800
project.funder.identifierhttp://doi.org/10.13039/501100001871
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
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.rightsclosedAccesspt_PT
rcaap.typearticlept_PT
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