Hanani triple systems View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1993-10

AUTHORS

S. A. Vanstone, D. R. Stinson, P. J. Schellenberg, A. Rosa, R. Rees, C. J. Colbourn, M. W. Carter, J. E. Carter

ABSTRACT

Hanani triple systems onv≡1 (mod 6) elements are Steiner triple systems having (v−1)/2 pairwise disjoint almost parallel classes (sets of pairwise disjoint triples that spanv−1 elements), and the remaining triples form a partial parallel class. Hanani triple systems are one natural analogue of the Kirkman triple systems onv≡3 (mod 6) elements, which form the solution of the celebrated Kirkman schoolgirl problem. We prove that a Hanani triple system exists for allv≡1 (mod 6) except forv ∈ {7, 13}. More... »

PAGES

305-319

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf02784058

DOI

http://dx.doi.org/10.1007/bf02784058

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1011887295


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/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Pure Mathematics", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada", 
          "id": "http://www.grid.ac/institutes/grid.46078.3d", 
          "name": [
            "Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Vanstone", 
        "givenName": "S. A.", 
        "id": "sg:person.010344544767.07", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010344544767.07"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Computer Science and Engineering, University of Nebraska, 68588, Lincoln, NE, USA", 
          "id": "http://www.grid.ac/institutes/grid.24434.35", 
          "name": [
            "Department of Computer Science and Engineering, University of Nebraska, 68588, Lincoln, NE, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Stinson", 
        "givenName": "D. R.", 
        "id": "sg:person.014151373147.58", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014151373147.58"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada", 
          "id": "http://www.grid.ac/institutes/grid.46078.3d", 
          "name": [
            "Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Schellenberg", 
        "givenName": "P. J.", 
        "id": "sg:person.011251054473.16", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011251054473.16"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Mathematics and Statistics, McMaster University, L8S 4K1, Hamilton, Ontario, Canada", 
          "id": "http://www.grid.ac/institutes/grid.25073.33", 
          "name": [
            "Department of Mathematics and Statistics, McMaster University, L8S 4K1, Hamilton, Ontario, Canada"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Rosa", 
        "givenName": "A.", 
        "id": "sg:person.010225567417.83", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010225567417.83"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Mathematics and Statistics, Memorial University of Newfoundland, A1C 5S7, St. John\u2019s, Newfoundland, Canada", 
          "id": "http://www.grid.ac/institutes/grid.25055.37", 
          "name": [
            "Department of Mathematics and Statistics, Memorial University of Newfoundland, A1C 5S7, St. John\u2019s, Newfoundland, Canada"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Rees", 
        "givenName": "R.", 
        "id": "sg:person.013106563242.56", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013106563242.56"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada", 
          "id": "http://www.grid.ac/institutes/grid.46078.3d", 
          "name": [
            "Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Colbourn", 
        "givenName": "C. J.", 
        "id": "sg:person.013304430047.53", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013304430047.53"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Industrial Engineering, University of Toronto, M5S 1A4, Toronto, Ontario, Canada", 
          "id": "http://www.grid.ac/institutes/grid.17063.33", 
          "name": [
            "Department of Industrial Engineering, University of Toronto, M5S 1A4, Toronto, Ontario, Canada"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Carter", 
        "givenName": "M. W.", 
        "id": "sg:person.01343101135.66", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01343101135.66"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Mathematics and Statistics, McMaster University, L8S 4K1, Hamilton, Ontario, Canada", 
          "id": "http://www.grid.ac/institutes/grid.25073.33", 
          "name": [
            "Department of Mathematics and Statistics, McMaster University, L8S 4K1, Hamilton, Ontario, Canada"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Carter", 
        "givenName": "J. E.", 
        "type": "Person"
      }
    ], 
    "datePublished": "1993-10", 
    "datePublishedReg": "1993-10-01", 
    "description": "Hanani triple systems onv\u22611 (mod 6) elements are Steiner triple systems having (v\u22121)/2 pairwise disjoint almost parallel classes (sets of pairwise disjoint triples that spanv\u22121 elements), and the remaining triples form a partial parallel class. Hanani triple systems are one natural analogue of the Kirkman triple systems onv\u22613 (mod 6) elements, which form the solution of the celebrated Kirkman schoolgirl problem. We prove that a Hanani triple system exists for allv\u22611 (mod 6) except forv \u2208 {7, 13}.", 
    "genre": "article", 
    "id": "sg:pub.10.1007/bf02784058", 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1136632", 
        "issn": [
          "0021-2172", 
          "1565-8511"
        ], 
        "name": "Israel Journal of Mathematics", 
        "publisher": "Springer Nature", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "3", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "83"
      }
    ], 
    "keywords": [
      "Steiner triple systems", 
      "system", 
      "elements", 
      "Kirkman triple systems", 
      "solution", 
      "natural analogues", 
      "Kirkman\u2019s Schoolgirl Problem", 
      "triple systems", 
      "problem", 
      "partial parallel classes", 
      "forv", 
      "class", 
      "parallel classes", 
      "analogues", 
      "triples", 
      "pairwise"
    ], 
    "name": "Hanani triple systems", 
    "pagination": "305-319", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1011887295"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/bf02784058"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/bf02784058", 
      "https://app.dimensions.ai/details/publication/pub.1011887295"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2022-12-01T06:19", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20221201/entities/gbq_results/article/article_227.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://doi.org/10.1007/bf02784058"
  }
]
 

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/bf02784058'

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/bf02784058'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf02784058'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf02784058'


 

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

133 TRIPLES      20 PREDICATES      41 URIs      33 LITERALS      6 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/bf02784058 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author Nc801d40849ad4655a9e123b9592e9c85
4 schema:datePublished 1993-10
5 schema:datePublishedReg 1993-10-01
6 schema:description Hanani triple systems onv≡1 (mod 6) elements are Steiner triple systems having (v−1)/2 pairwise disjoint almost parallel classes (sets of pairwise disjoint triples that spanv−1 elements), and the remaining triples form a partial parallel class. Hanani triple systems are one natural analogue of the Kirkman triple systems onv≡3 (mod 6) elements, which form the solution of the celebrated Kirkman schoolgirl problem. We prove that a Hanani triple system exists for allv≡1 (mod 6) except forv ∈ {7, 13}.
7 schema:genre article
8 schema:isAccessibleForFree false
9 schema:isPartOf N64049fc8950d4a68a1257435e372b968
10 N715232db778546739fac0ff24e6009ce
11 sg:journal.1136632
12 schema:keywords Kirkman triple systems
13 Kirkman’s Schoolgirl Problem
14 Steiner triple systems
15 analogues
16 class
17 elements
18 forv
19 natural analogues
20 pairwise
21 parallel classes
22 partial parallel classes
23 problem
24 solution
25 system
26 triple systems
27 triples
28 schema:name Hanani triple systems
29 schema:pagination 305-319
30 schema:productId N69adb810a52045c68e6acc95108955db
31 Nb417a9e6ccaa4bd6920d053a5d587d73
32 schema:sameAs https://app.dimensions.ai/details/publication/pub.1011887295
33 https://doi.org/10.1007/bf02784058
34 schema:sdDatePublished 2022-12-01T06:19
35 schema:sdLicense https://scigraph.springernature.com/explorer/license/
36 schema:sdPublisher N791fa705f3524aa8a7e15bea38d01764
37 schema:url https://doi.org/10.1007/bf02784058
38 sgo:license sg:explorer/license/
39 sgo:sdDataset articles
40 rdf:type schema:ScholarlyArticle
41 N0b5aa50ff27d4ab887f6b30be6a5b1a0 rdf:first N438297b0db984884a9ad5ae0e6e7802d
42 rdf:rest rdf:nil
43 N3ef5f8fce85b476087e508e1cdcf81a5 rdf:first sg:person.013304430047.53
44 rdf:rest N8ff066efce474449af4f78bd58e39f47
45 N438297b0db984884a9ad5ae0e6e7802d schema:affiliation grid-institutes:grid.25073.33
46 schema:familyName Carter
47 schema:givenName J. E.
48 rdf:type schema:Person
49 N521bc0d64eca4b54980ebd1a049ca505 rdf:first sg:person.013106563242.56
50 rdf:rest N3ef5f8fce85b476087e508e1cdcf81a5
51 N64049fc8950d4a68a1257435e372b968 schema:issueNumber 3
52 rdf:type schema:PublicationIssue
53 N69adb810a52045c68e6acc95108955db schema:name doi
54 schema:value 10.1007/bf02784058
55 rdf:type schema:PropertyValue
56 N6f718af13a334d7fa3d3462251daec90 rdf:first sg:person.011251054473.16
57 rdf:rest N7a384d625e734deeaac424c2846a26ab
58 N715232db778546739fac0ff24e6009ce schema:volumeNumber 83
59 rdf:type schema:PublicationVolume
60 N791fa705f3524aa8a7e15bea38d01764 schema:name Springer Nature - SN SciGraph project
61 rdf:type schema:Organization
62 N7a384d625e734deeaac424c2846a26ab rdf:first sg:person.010225567417.83
63 rdf:rest N521bc0d64eca4b54980ebd1a049ca505
64 N8ff066efce474449af4f78bd58e39f47 rdf:first sg:person.01343101135.66
65 rdf:rest N0b5aa50ff27d4ab887f6b30be6a5b1a0
66 Nb2f8d5b208354386a49532a75f7d6caf rdf:first sg:person.014151373147.58
67 rdf:rest N6f718af13a334d7fa3d3462251daec90
68 Nb417a9e6ccaa4bd6920d053a5d587d73 schema:name dimensions_id
69 schema:value pub.1011887295
70 rdf:type schema:PropertyValue
71 Nc801d40849ad4655a9e123b9592e9c85 rdf:first sg:person.010344544767.07
72 rdf:rest Nb2f8d5b208354386a49532a75f7d6caf
73 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
74 schema:name Mathematical Sciences
75 rdf:type schema:DefinedTerm
76 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
77 schema:name Pure Mathematics
78 rdf:type schema:DefinedTerm
79 sg:journal.1136632 schema:issn 0021-2172
80 1565-8511
81 schema:name Israel Journal of Mathematics
82 schema:publisher Springer Nature
83 rdf:type schema:Periodical
84 sg:person.010225567417.83 schema:affiliation grid-institutes:grid.25073.33
85 schema:familyName Rosa
86 schema:givenName A.
87 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010225567417.83
88 rdf:type schema:Person
89 sg:person.010344544767.07 schema:affiliation grid-institutes:grid.46078.3d
90 schema:familyName Vanstone
91 schema:givenName S. A.
92 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010344544767.07
93 rdf:type schema:Person
94 sg:person.011251054473.16 schema:affiliation grid-institutes:grid.46078.3d
95 schema:familyName Schellenberg
96 schema:givenName P. J.
97 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011251054473.16
98 rdf:type schema:Person
99 sg:person.013106563242.56 schema:affiliation grid-institutes:grid.25055.37
100 schema:familyName Rees
101 schema:givenName R.
102 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013106563242.56
103 rdf:type schema:Person
104 sg:person.013304430047.53 schema:affiliation grid-institutes:grid.46078.3d
105 schema:familyName Colbourn
106 schema:givenName C. J.
107 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013304430047.53
108 rdf:type schema:Person
109 sg:person.01343101135.66 schema:affiliation grid-institutes:grid.17063.33
110 schema:familyName Carter
111 schema:givenName M. W.
112 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01343101135.66
113 rdf:type schema:Person
114 sg:person.014151373147.58 schema:affiliation grid-institutes:grid.24434.35
115 schema:familyName Stinson
116 schema:givenName D. R.
117 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014151373147.58
118 rdf:type schema:Person
119 grid-institutes:grid.17063.33 schema:alternateName Department of Industrial Engineering, University of Toronto, M5S 1A4, Toronto, Ontario, Canada
120 schema:name Department of Industrial Engineering, University of Toronto, M5S 1A4, Toronto, Ontario, Canada
121 rdf:type schema:Organization
122 grid-institutes:grid.24434.35 schema:alternateName Department of Computer Science and Engineering, University of Nebraska, 68588, Lincoln, NE, USA
123 schema:name Department of Computer Science and Engineering, University of Nebraska, 68588, Lincoln, NE, USA
124 rdf:type schema:Organization
125 grid-institutes:grid.25055.37 schema:alternateName Department of Mathematics and Statistics, Memorial University of Newfoundland, A1C 5S7, St. John’s, Newfoundland, Canada
126 schema:name Department of Mathematics and Statistics, Memorial University of Newfoundland, A1C 5S7, St. John’s, Newfoundland, Canada
127 rdf:type schema:Organization
128 grid-institutes:grid.25073.33 schema:alternateName Department of Mathematics and Statistics, McMaster University, L8S 4K1, Hamilton, Ontario, Canada
129 schema:name Department of Mathematics and Statistics, McMaster University, L8S 4K1, Hamilton, Ontario, Canada
130 rdf:type schema:Organization
131 grid-institutes:grid.46078.3d schema:alternateName Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada
132 schema:name Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada
133 rdf:type schema:Organization
 




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


...