Publicação
Some notes on disjunctive short sum: polychromatic nim
| datacite.subject.fos | Ciências Naturais::Matemáticas | |
| dc.contributor.author | Carvalho, Alda | |
| dc.contributor.author | Santos, Carlos Pereira dos | |
| dc.date.accessioned | 2026-01-29T11:35:02Z | |
| dc.date.available | 2026-01-29T11:35:02Z | |
| dc.date.issued | 2023 | |
| dc.description.abstract | polychromatic nim is a version of the classic game nim, played with colored stones, in which each pile has stones of a single color, and the player who successfully extinguishes a color wins the game. This game is closely related to the concept of short rule, the ending condition that states that a disjunctive sum ends as soon as any one of the components ends. Here, we discuss that rule, namely when applied to impartial games, and prove that the Grundy-values of polychromatic nim present an arithmetic-periodic behavior. | eng |
| dc.description.sponsorship | Alda Carvalho is a CEMAPRE member and has the support of Project CEMAPRE/REM - UIDB/05069/2020 financed by FCT/MCTES, Portugal through national funds. Carlos Santos work is funded by national funds through the FCT - Fundação para a Ciência e a Tecnologia, I.P. , Portugal, under the scope of the projects UIDB/00297/2020 and UIDP/00297/2020 (Center for Mathematics and Applications). | |
| dc.identifier.doi | 10.1016/j.dam.2022.09.018 | |
| dc.identifier.issn | 0166-218X | |
| dc.identifier.uri | http://hdl.handle.net/10400.2/21086 | |
| dc.language.iso | eng | |
| dc.peerreviewed | yes | |
| dc.publisher | Elsevier | |
| dc.relation | Research in Economics and Mathematics | |
| dc.relation | Center for Mathematics and Applications | |
| dc.relation.hasversion | https://www.sciencedirect.com/science/article/pii/S0166218X22003663?via%3Dihub | |
| dc.rights.uri | N/A | |
| dc.subject | Combinatorial game theory | |
| dc.subject | Disjunctive short sum | |
| dc.subject | Impartial games | |
| dc.subject | Sprague–Grundy theory | |
| dc.subject | Arithmetic periodicity | |
| dc.subject | Polychromatic nim | |
| dc.title | Some notes on disjunctive short sum: polychromatic nim | eng |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.awardTitle | Research in Economics and Mathematics | |
| oaire.awardTitle | Center for Mathematics and Applications | |
| oaire.awardURI | http://hdl.handle.net/10400.2/21084 | |
| oaire.awardURI | info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00297%2F2020/PT | |
| oaire.citation.endPage | 125 | |
| oaire.citation.startPage | 113 | |
| oaire.citation.title | Discrete Applied Mathematics | |
| oaire.citation.volume | 324 | |
| oaire.fundingStream | Concurso de avaliação no âmbito do Programa Plurianual de Financiamento de Unidades de I&D (2017/2018) - Financiamento Base | |
| oaire.fundingStream | 6817 - DCRRNI ID | |
| oaire.version | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |
| person.familyName | Carvalho | |
| person.givenName | Alda | |
| person.identifier | AAA-4372-2021 | |
| person.identifier.ciencia-id | FD18-CBDD-B7C7 | |
| person.identifier.orcid | 0000-0003-2642-4947 | |
| person.identifier.scopus-author-id | 25027091800 | |
| project.funder.identifier | http://doi.org/10.13039/501100001871 | |
| project.funder.name | Fundação para a Ciência e a Tecnologia | |
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