You are here:   
  1. Home
  2. Articles
  3. http://scigraph.springernature.com/pub.10.1007/s10623-020-00725-y

On the number of resolvable Steiner triple systems of small 3-rank View Full Text

Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2020-02-04

AUTHORS

Minjia Shi, Li Xu, Denis S. Krotov

ABSTRACT

In a recent work, Jungnickel, Magliveras, Tonchev, and Wassermann derived an overexponential lower bound on the number of nonisomorphic resolvable Steiner triple systems (STS) of order v, where v=3k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v=3^k$$\end{document}, and 3-rank v-k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v-k$$\end{document}. We develop an approach to generalize this bound and estimate the number of isomorphism classes of resolvable STS (v) of 3-rank v-k-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v-k-1$$\end{document} for an arbitrary v of form 3kT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3^kT$$\end{document}, where T is congruent to 1 or 3 modulo 6. More... »

PAGES

1037-1046

References to SciGraph publications

  • 2017-09-02. On Bonisoli’s theorem and the block codes of Steiner triple systems in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2018-06-15. The classification of Steiner triple systems on 27 points with 3-rank 24 in DESIGNS, CODES AND CRYPTOGRAPHY
  • 1978-10. Ranks of incidence matrices of Steiner triple systems in MATHEMATISCHE ZEITSCHRIFT

    • Journal

    TITLE

    Designs, Codes and Cryptography

    ISSUE

    6

    VOLUME

    88

    Subjects

  • FOR: Information And Computing Sciences
  • FOR: Artificial Intelligence And Image Processing

    • Author Affiliations

  • Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Mathematical Sciences, Anhui University, 230601, Hefei, Anhui, China
  • School of Mathematical Sciences, Anhui University, 230601, Hefei, Anhui, China
  • Sobolev Institute of Mathematics, pr. Akademika Koptyuga 4, 630090, Novosibirsk, Russia

    • From Grant

  • Research On N-Weight Code On Finite Ring And Its Application

    • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10623-020-00725-y

    DOI

    http://dx.doi.org/10.1007/s10623-020-00725-y

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1124588179

    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/2008/08", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Information and Computing Sciences", 
        "type": "DefinedTerm"
      }, 
      {
        "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"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Mathematical Sciences, Anhui University, 230601, Hefei, Anhui, China", 
          "id": "http://www.grid.ac/institutes/grid.252245.6", 
          "name": [
            "Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Mathematical Sciences, Anhui University, 230601, Hefei, Anhui, China"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Shi", 
        "givenName": "Minjia", 
        "id": "sg:person.012012432235.16", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012012432235.16"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "School of Mathematical Sciences, Anhui University, 230601, Hefei, Anhui, China", 
          "id": "http://www.grid.ac/institutes/grid.252245.6", 
          "name": [
            "School of Mathematical Sciences, Anhui University, 230601, Hefei, Anhui, China"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Xu", 
        "givenName": "Li", 
        "id": "sg:person.014463040757.81", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014463040757.81"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Sobolev Institute of Mathematics, pr. Akademika Koptyuga 4, 630090, Novosibirsk, Russia", 
          "id": "http://www.grid.ac/institutes/grid.426295.e", 
          "name": [
            "Sobolev Institute of Mathematics, pr. Akademika Koptyuga 4, 630090, Novosibirsk, Russia"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Krotov", 
        "givenName": "Denis S.", 
        "id": "sg:person.013674271021.75", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013674271021.75"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/s10623-017-0406-9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1091424654", 
          "https://doi.org/10.1007/s10623-017-0406-9"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s10623-018-0502-5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1104646273", 
          "https://doi.org/10.1007/s10623-018-0502-5"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01174898", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1042478746", 
          "https://doi.org/10.1007/bf01174898"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2020-02-04", 
    "datePublishedReg": "2020-02-04", 
    "description": "In a recent work, Jungnickel, Magliveras, Tonchev, and Wassermann derived an overexponential lower bound on the number of nonisomorphic resolvable Steiner triple systems (STS) of order v, where v=3k\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$v=3^k$$\\end{document}, and 3-rank v-k\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$v-k$$\\end{document}. We develop an approach to generalize this bound and estimate the number of isomorphism classes of resolvable STS (v) of 3-rank v-k-1\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$v-k-1$$\\end{document} for an arbitrary v of form 3kT\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$3^kT$$\\end{document}, where T is congruent to 1 or 3 modulo 6.", 
    "genre": "article", 
    "id": "sg:pub.10.1007/s10623-020-00725-y", 
    "inLanguage": "en", 
    "isAccessibleForFree": true, 
    "isFundedItemOf": [
      {
        "id": "sg:grant.8306127", 
        "type": "MonetaryGrant"
      }
    ], 
    "isPartOf": [
      {
        "id": "sg:journal.1136552", 
        "issn": [
          "0925-1022", 
          "1573-7586"
        ], 
        "name": "Designs, Codes and Cryptography", 
        "publisher": "Springer Nature", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "6", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "88"
      }
    ], 
    "keywords": [
      "Steiner triple systems", 
      "triple systems", 
      "isomorphism classes", 
      "modulo 6", 
      "Magliveras", 
      "order v", 
      "Tonchev", 
      "recent work", 
      "Jungnickel", 
      "number", 
      "system", 
      "class", 
      "approach", 
      "form", 
      "work", 
      "Wassermann", 
      "congruent"
    ], 
    "name": "On the number of resolvable Steiner triple systems of small 3-rank", 
    "pagination": "1037-1046", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1124588179"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s10623-020-00725-y"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s10623-020-00725-y", 
      "https://app.dimensions.ai/details/publication/pub.1124588179"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2022-05-10T10:26", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20220509/entities/gbq_results/article/article_859.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://doi.org/10.1007/s10623-020-00725-y"
  }
]
     

    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/s10623-020-00725-y'

    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/s10623-020-00725-y'

    Turtle is a human-readable linked data format. 

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s10623-020-00725-y'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s10623-020-00725-y'


     

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

    108 TRIPLES      22 PREDICATES      45 URIs      34 LITERALS      6 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s10623-020-00725-y schema:about anzsrc-for:08
    2 ″ ″ anzsrc-for:0801
    3 ″ schema:author N2004ab3e672b4049bce8ee6972b1e458
    4 ″ schema:citation sg:pub.10.1007/bf01174898
    5 ″ ″ sg:pub.10.1007/s10623-017-0406-9
    6 ″ ″ sg:pub.10.1007/s10623-018-0502-5
    7 ″ schema:datePublished 2020-02-04
    8 ″ schema:datePublishedReg 2020-02-04
    9 ″ schema:description In a recent work, Jungnickel, Magliveras, Tonchev, and Wassermann derived an overexponential lower bound on the number of nonisomorphic resolvable Steiner triple systems (STS) of order v, where v=3k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v=3^k$$\end{document}, and 3-rank v-k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v-k$$\end{document}. We develop an approach to generalize this bound and estimate the number of isomorphism classes of resolvable STS (v) of 3-rank v-k-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v-k-1$$\end{document} for an arbitrary v of form 3kT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3^kT$$\end{document}, where T is congruent to 1 or 3 modulo 6.
    10 ″ schema:genre article
    11 ″ schema:inLanguage en
    12 ″ schema:isAccessibleForFree true
    13 ″ schema:isPartOf N29051a2c77cb459592fe2a29c05fdd29
    14 ″ ″ N3229aad7354744fba759005851b340fe
    15 ″ ″ sg:journal.1136552
    16 ″ schema:keywords Jungnickel
    17 ″ ″ Magliveras
    18 ″ ″ Steiner triple systems
    19 ″ ″ Tonchev
    20 ″ ″ Wassermann
    21 ″ ″ approach
    22 ″ ″ class
    23 ″ ″ congruent
    24 ″ ″ form
    25 ″ ″ isomorphism classes
    26 ″ ″ modulo 6
    27 ″ ″ number
    28 ″ ″ order v
    29 ″ ″ recent work
    30 ″ ″ system
    31 ″ ″ triple systems
    32 ″ ″ work
    33 ″ schema:name On the number of resolvable Steiner triple systems of small 3-rank
    34 ″ schema:pagination 1037-1046
    35 ″ schema:productId N233d09517bf74c229277501b3d15a4b5
    36 ″ ″ N5ec68edbd36b43bb894826ed8cc824b2
    37 ″ schema:sameAs https://app.dimensions.ai/details/publication/pub.1124588179
    38 ″ ″ https://doi.org/10.1007/s10623-020-00725-y
    39 ″ schema:sdDatePublished 2022-05-10T10:26
    40 ″ schema:sdLicense https://scigraph.springernature.com/explorer/license/
    41 ″ schema:sdPublisher N65596531f4024ea1b8c944a97461255c
    42 ″ schema:url https://doi.org/10.1007/s10623-020-00725-y
    43 ″ sgo:license sg:explorer/license/
    44 ″ sgo:sdDataset articles
    45 ″ rdf:type schema:ScholarlyArticle
    46 N2004ab3e672b4049bce8ee6972b1e458 rdf:first sg:person.012012432235.16
    47 ″ rdf:rest Nd058773a941f4c5aa8d82cea54a6c0b6
    48 N233d09517bf74c229277501b3d15a4b5 schema:name dimensions_id
    49 ″ schema:value pub.1124588179
    50 ″ rdf:type schema:PropertyValue
    51 N29051a2c77cb459592fe2a29c05fdd29 schema:volumeNumber 88
    52 ″ rdf:type schema:PublicationVolume
    53 N3229aad7354744fba759005851b340fe schema:issueNumber 6
    54 ″ rdf:type schema:PublicationIssue
    55 N5ec68edbd36b43bb894826ed8cc824b2 schema:name doi
    56 ″ schema:value 10.1007/s10623-020-00725-y
    57 ″ rdf:type schema:PropertyValue
    58 N65596531f4024ea1b8c944a97461255c schema:name Springer Nature - SN SciGraph project
    59 ″ rdf:type schema:Organization
    60 Nc20516724d4f40a9b37f796767fdd85b rdf:first sg:person.013674271021.75
    61 ″ rdf:rest rdf:nil
    62 Nd058773a941f4c5aa8d82cea54a6c0b6 rdf:first sg:person.014463040757.81
    63 ″ rdf:rest Nc20516724d4f40a9b37f796767fdd85b
    64 anzsrc-for:08 schema:inDefinedTermSet anzsrc-for:
    65 ″ schema:name Information and Computing Sciences
    66 ″ rdf:type schema:DefinedTerm
    67 anzsrc-for:0801 schema:inDefinedTermSet anzsrc-for:
    68 ″ schema:name Artificial Intelligence and Image Processing
    69 ″ rdf:type schema:DefinedTerm
    70 sg:grant.8306127 http://pending.schema.org/fundedItem sg:pub.10.1007/s10623-020-00725-y
    71 ″ rdf:type schema:MonetaryGrant
    72 sg:journal.1136552 schema:issn 0925-1022
    73 ″ ″ 1573-7586
    74 ″ schema:name Designs, Codes and Cryptography
    75 ″ schema:publisher Springer Nature
    76 ″ rdf:type schema:Periodical
    77 sg:person.012012432235.16 schema:affiliation grid-institutes:grid.252245.6
    78 ″ schema:familyName Shi
    79 ″ schema:givenName Minjia
    80 ″ schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012012432235.16
    81 ″ rdf:type schema:Person
    82 sg:person.013674271021.75 schema:affiliation grid-institutes:grid.426295.e
    83 ″ schema:familyName Krotov
    84 ″ schema:givenName Denis S.
    85 ″ schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013674271021.75
    86 ″ rdf:type schema:Person
    87 sg:person.014463040757.81 schema:affiliation grid-institutes:grid.252245.6
    88 ″ schema:familyName Xu
    89 ″ schema:givenName Li
    90 ″ schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014463040757.81
    91 ″ rdf:type schema:Person
    92 sg:pub.10.1007/bf01174898 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042478746
    93 ″ ″ https://doi.org/10.1007/bf01174898
    94 ″ rdf:type schema:CreativeWork
    95 sg:pub.10.1007/s10623-017-0406-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1091424654
    96 ″ ″ https://doi.org/10.1007/s10623-017-0406-9
    97 ″ rdf:type schema:CreativeWork
    98 sg:pub.10.1007/s10623-018-0502-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1104646273
    99 ″ ″ https://doi.org/10.1007/s10623-018-0502-5
    100 ″ rdf:type schema:CreativeWork
    101 grid-institutes:grid.252245.6 schema:alternateName Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Mathematical Sciences, Anhui University, 230601, Hefei, Anhui, China
    102 ″ ″ School of Mathematical Sciences, Anhui University, 230601, Hefei, Anhui, China
    103 ″ schema:name Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Mathematical Sciences, Anhui University, 230601, Hefei, Anhui, China
    104 ″ ″ School of Mathematical Sciences, Anhui University, 230601, Hefei, Anhui, China
    105 ″ rdf:type schema:Organization
    106 grid-institutes:grid.426295.e schema:alternateName Sobolev Institute of Mathematics, pr. Akademika Koptyuga 4, 630090, Novosibirsk, Russia
    107 ″ schema:name Sobolev Institute of Mathematics, pr. Akademika Koptyuga 4, 630090, Novosibirsk, Russia
    108 ″ rdf:type schema:Organization
     




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

    ...