Impartial achievement and avoidance games for generating finite groups View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2018-05

AUTHORS

Dana C. Ernst, Nándor Sieben

ABSTRACT

We study two impartial games introduced by Anderson and Harary and further developed by Barnes. Both games are played by two players who alternately select previously unselected elements of a finite group. The first player who builds a generating set from the jointly selected elements wins the first game. The first player who cannot select an element without building a generating set loses the second game. After the development of some general results, we determine the nim-numbers of these games for abelian and dihedral groups. We also present some conjectures based on computer calculations. Our main computational and theoretical tool is the structure diagram of a game, which is a type of identification digraph of the game digraph that is compatible with the nim-numbers of the positions. Structure diagrams also provide simple yet intuitive visualizations of these games that capture the complexity of the positions. More... »

PAGES

509-542

References to SciGraph publications

  • 2018-05. Algebraic games—playing with groups and rings in INTERNATIONAL JOURNAL OF GAME THEORY
  • 1987-12. Achievement and avoidance games for generating abelian groups in INTERNATIONAL JOURNAL OF GAME THEORY
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00182-017-0602-x

    DOI

    http://dx.doi.org/10.1007/s00182-017-0602-x

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1099700060


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0801", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Artificial Intelligence and Image Processing", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/08", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Information and Computing Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Northern Arizona University", 
              "id": "https://www.grid.ac/institutes/grid.261120.6", 
              "name": [
                "Department of Mathematics and Statistics, Northern Arizona University, 86011-5717, Flagstaff, AZ, USA"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Ernst", 
            "givenName": "Dana C.", 
            "id": "sg:person.014752501111.52", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014752501111.52"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Northern Arizona University", 
              "id": "https://www.grid.ac/institutes/grid.261120.6", 
              "name": [
                "Department of Mathematics and Statistics, Northern Arizona University, 86011-5717, Flagstaff, AZ, USA"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Sieben", 
            "givenName": "N\u00e1ndor", 
            "id": "sg:person.0705654574.72", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0705654574.72"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "https://doi.org/10.1016/s0021-9800(66)80005-4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1005447706"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01756028", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1030098037", 
              "https://doi.org/10.1007/bf01756028"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01756028", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1030098037", 
              "https://doi.org/10.1007/bf01756028"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00182-017-0577-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1085110753", 
              "https://doi.org/10.1007/s00182-017-0577-7"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00182-017-0577-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1085110753", 
              "https://doi.org/10.1007/s00182-017-0577-7"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/gsm/146", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1098468182"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2018-05", 
        "datePublishedReg": "2018-05-01", 
        "description": "We study two impartial games introduced by Anderson and Harary and further developed by Barnes. Both games are played by two players who alternately select previously unselected elements of a finite group. The first player who builds a generating set from the jointly selected elements wins the first game. The first player who cannot select an element without building a generating set loses the second game. After the development of some general results, we determine the nim-numbers of these games for abelian and dihedral groups. We also present some conjectures based on computer calculations. Our main computational and theoretical tool is the structure diagram of a game, which is a type of identification digraph of the game digraph that is compatible with the nim-numbers of the positions. Structure diagrams also provide simple yet intuitive visualizations of these games that capture the complexity of the positions.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/s00182-017-0602-x", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": true, 
        "isPartOf": [
          {
            "id": "sg:journal.1136357", 
            "issn": [
              "0020-7276", 
              "1432-1270"
            ], 
            "name": "International Journal of Game Theory", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "2", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "47"
          }
        ], 
        "name": "Impartial achievement and avoidance games for generating finite groups", 
        "pagination": "509-542", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "a6daf8c7b4ed7279a8e46ae4e19f9592fee784dee66bb4b0ba605e8a95005c0a"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s00182-017-0602-x"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1099700060"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s00182-017-0602-x", 
          "https://app.dimensions.ai/details/publication/pub.1099700060"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-10T17:44", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000001_0000000264/records_8672_00000603.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "http://link.springer.com/10.1007/s00182-017-0602-x"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s00182-017-0602-x'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s00182-017-0602-x'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00182-017-0602-x'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00182-017-0602-x'


     

    This table displays all metadata directly associated to this object as RDF triples.

    82 TRIPLES      21 PREDICATES      31 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s00182-017-0602-x schema:about anzsrc-for:08
    2 anzsrc-for:0801
    3 schema:author N5145aca3da2c423e8b9c918d68a0da72
    4 schema:citation sg:pub.10.1007/bf01756028
    5 sg:pub.10.1007/s00182-017-0577-7
    6 https://doi.org/10.1016/s0021-9800(66)80005-4
    7 https://doi.org/10.1090/gsm/146
    8 schema:datePublished 2018-05
    9 schema:datePublishedReg 2018-05-01
    10 schema:description We study two impartial games introduced by Anderson and Harary and further developed by Barnes. Both games are played by two players who alternately select previously unselected elements of a finite group. The first player who builds a generating set from the jointly selected elements wins the first game. The first player who cannot select an element without building a generating set loses the second game. After the development of some general results, we determine the nim-numbers of these games for abelian and dihedral groups. We also present some conjectures based on computer calculations. Our main computational and theoretical tool is the structure diagram of a game, which is a type of identification digraph of the game digraph that is compatible with the nim-numbers of the positions. Structure diagrams also provide simple yet intuitive visualizations of these games that capture the complexity of the positions.
    11 schema:genre research_article
    12 schema:inLanguage en
    13 schema:isAccessibleForFree true
    14 schema:isPartOf N20b84359d5df489b97f0ca04451f5dad
    15 N731e039923d64901a35c88d139861e8d
    16 sg:journal.1136357
    17 schema:name Impartial achievement and avoidance games for generating finite groups
    18 schema:pagination 509-542
    19 schema:productId N608fdb7976f843d59b192cfc07d7d347
    20 Nca049f5e68ea46528f8fb80405d5528f
    21 Nca92cae54341427da0038dad7fc15ac4
    22 schema:sameAs https://app.dimensions.ai/details/publication/pub.1099700060
    23 https://doi.org/10.1007/s00182-017-0602-x
    24 schema:sdDatePublished 2019-04-10T17:44
    25 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    26 schema:sdPublisher Nea4a18518f344da4882fc6ae3143db45
    27 schema:url http://link.springer.com/10.1007/s00182-017-0602-x
    28 sgo:license sg:explorer/license/
    29 sgo:sdDataset articles
    30 rdf:type schema:ScholarlyArticle
    31 N20b84359d5df489b97f0ca04451f5dad schema:volumeNumber 47
    32 rdf:type schema:PublicationVolume
    33 N4f68f0ac239e4cbfbf71ca67aa52a4b6 rdf:first sg:person.0705654574.72
    34 rdf:rest rdf:nil
    35 N5145aca3da2c423e8b9c918d68a0da72 rdf:first sg:person.014752501111.52
    36 rdf:rest N4f68f0ac239e4cbfbf71ca67aa52a4b6
    37 N608fdb7976f843d59b192cfc07d7d347 schema:name doi
    38 schema:value 10.1007/s00182-017-0602-x
    39 rdf:type schema:PropertyValue
    40 N731e039923d64901a35c88d139861e8d schema:issueNumber 2
    41 rdf:type schema:PublicationIssue
    42 Nca049f5e68ea46528f8fb80405d5528f schema:name dimensions_id
    43 schema:value pub.1099700060
    44 rdf:type schema:PropertyValue
    45 Nca92cae54341427da0038dad7fc15ac4 schema:name readcube_id
    46 schema:value a6daf8c7b4ed7279a8e46ae4e19f9592fee784dee66bb4b0ba605e8a95005c0a
    47 rdf:type schema:PropertyValue
    48 Nea4a18518f344da4882fc6ae3143db45 schema:name Springer Nature - SN SciGraph project
    49 rdf:type schema:Organization
    50 anzsrc-for:08 schema:inDefinedTermSet anzsrc-for:
    51 schema:name Information and Computing Sciences
    52 rdf:type schema:DefinedTerm
    53 anzsrc-for:0801 schema:inDefinedTermSet anzsrc-for:
    54 schema:name Artificial Intelligence and Image Processing
    55 rdf:type schema:DefinedTerm
    56 sg:journal.1136357 schema:issn 0020-7276
    57 1432-1270
    58 schema:name International Journal of Game Theory
    59 rdf:type schema:Periodical
    60 sg:person.014752501111.52 schema:affiliation https://www.grid.ac/institutes/grid.261120.6
    61 schema:familyName Ernst
    62 schema:givenName Dana C.
    63 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014752501111.52
    64 rdf:type schema:Person
    65 sg:person.0705654574.72 schema:affiliation https://www.grid.ac/institutes/grid.261120.6
    66 schema:familyName Sieben
    67 schema:givenName Nándor
    68 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0705654574.72
    69 rdf:type schema:Person
    70 sg:pub.10.1007/bf01756028 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030098037
    71 https://doi.org/10.1007/bf01756028
    72 rdf:type schema:CreativeWork
    73 sg:pub.10.1007/s00182-017-0577-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1085110753
    74 https://doi.org/10.1007/s00182-017-0577-7
    75 rdf:type schema:CreativeWork
    76 https://doi.org/10.1016/s0021-9800(66)80005-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005447706
    77 rdf:type schema:CreativeWork
    78 https://doi.org/10.1090/gsm/146 schema:sameAs https://app.dimensions.ai/details/publication/pub.1098468182
    79 rdf:type schema:CreativeWork
    80 https://www.grid.ac/institutes/grid.261120.6 schema:alternateName Northern Arizona University
    81 schema:name Department of Mathematics and Statistics, Northern Arizona University, 86011-5717, Flagstaff, AZ, USA
    82 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...