Largest induced suborders satisfying the chain condition View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

1985-09

AUTHORS

Nathan Linial, Michael Saks, Peter Shor

ABSTRACT

For a finite ordered set P, let c(P) denote the cardinality of the largest subset Q such that the induced suborder on Q satisfies the Jordan-Dedekind chain condition (JDCC), i.e., every maximal chain in Q has the same cardinality. For positive integers n, let f(n) be the minimum of c(P) over all ordered sets P of cardinality n. We prove: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\sqrt {2n } - 1 \leqslant f (n) \leqslant 4 e \sqrt {n.}$$ \end{document} More... »

PAGES

265-268

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf00333132

DOI

http://dx.doi.org/10.1007/bf00333132

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1085566283


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 Computer Science, Hebrew University, Jerusalem, Israel", 
          "id": "http://www.grid.ac/institutes/grid.9619.7", 
          "name": [
            "Department of Computer Science, Hebrew University, Jerusalem, Israel"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Linial", 
        "givenName": "Nathan", 
        "id": "sg:person.015760032537.47", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015760032537.47"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Bell Communications Research, 435 South St., 07960, Morristown, NJ, USA", 
          "id": "http://www.grid.ac/institutes/grid.432790.b", 
          "name": [
            "Bell Communications Research, 435 South St., 07960, Morristown, NJ, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Saks", 
        "givenName": "Michael", 
        "id": "sg:person.011520224512.05", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011520224512.05"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Mathematics, MIT, 02139, Cambridge, MA, USA", 
          "id": "http://www.grid.ac/institutes/grid.116068.8", 
          "name": [
            "Department of Mathematics, MIT, 02139, Cambridge, MA, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Shor", 
        "givenName": "Peter", 
        "id": "sg:person.0727564714.69", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0727564714.69"
        ], 
        "type": "Person"
      }
    ], 
    "datePublished": "1985-09", 
    "datePublishedReg": "1985-09-01", 
    "description": "For a finite ordered set P, let c(P) denote the cardinality of the largest subset Q such that the induced suborder on Q satisfies the Jordan-Dedekind chain condition (JDCC), i.e., every maximal chain in Q has the same cardinality. For positive integers n, let f(n) be the minimum of c(P) over all ordered sets P of cardinality n. We prove: \\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}\n$$\\sqrt {2n }  -  1  \\leqslant  f (n)  \\leqslant  4 e \\sqrt {n.}$$\n\\end{document}", 
    "genre": "article", 
    "id": "sg:pub.10.1007/bf00333132", 
    "isAccessibleForFree": true, 
    "isPartOf": [
      {
        "id": "sg:journal.1136683", 
        "issn": [
          "0167-8094", 
          "1572-9273"
        ], 
        "name": "Order", 
        "publisher": "Springer Nature", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "3", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "2"
      }
    ], 
    "keywords": [
      "Jordan-Dedekind chain condition", 
      "conditions", 
      "minimum", 
      "chain", 
      "subset Q", 
      "suborders", 
      "q satisfies", 
      "chain condition", 
      "maximal chains", 
      "same cardinality", 
      "positive integer n", 
      "set P", 
      "finite", 
      "cardinality", 
      "satisfies", 
      "integer n", 
      "cardinality n.", 
      "n."
    ], 
    "name": "Largest induced suborders satisfying the chain condition", 
    "pagination": "265-268", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1085566283"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/bf00333132"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/bf00333132", 
      "https://app.dimensions.ai/details/publication/pub.1085566283"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2022-09-02T15:45", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20220902/entities/gbq_results/article/article_187.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://doi.org/10.1007/bf00333132"
  }
]
 

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/bf00333132'

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/bf00333132'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf00333132'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf00333132'


 

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

95 TRIPLES      20 PREDICATES      43 URIs      35 LITERALS      6 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/bf00333132 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author N87f7d87236c44074b7b5603bd81b6d21
4 schema:datePublished 1985-09
5 schema:datePublishedReg 1985-09-01
6 schema:description For a finite ordered set P, let c(P) denote the cardinality of the largest subset Q such that the induced suborder on Q satisfies the Jordan-Dedekind chain condition (JDCC), i.e., every maximal chain in Q has the same cardinality. For positive integers n, let f(n) be the minimum of c(P) over all ordered sets P of cardinality n. We prove: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\sqrt {2n } - 1 \leqslant f (n) \leqslant 4 e \sqrt {n.}$$ \end{document}
7 schema:genre article
8 schema:isAccessibleForFree true
9 schema:isPartOf N4c7746291b564aaca05c0c77cec792b7
10 Ne3366a5779a54ae8856d9911f57ad34b
11 sg:journal.1136683
12 schema:keywords Jordan-Dedekind chain condition
13 cardinality
14 cardinality n.
15 chain
16 chain condition
17 conditions
18 finite
19 integer n
20 maximal chains
21 minimum
22 n.
23 positive integer n
24 q satisfies
25 same cardinality
26 satisfies
27 set P
28 suborders
29 subset Q
30 schema:name Largest induced suborders satisfying the chain condition
31 schema:pagination 265-268
32 schema:productId N818bd132b9244ae4a8084e4d89dae416
33 Nf2f8831a35a14edea4795b3c2b29c9ff
34 schema:sameAs https://app.dimensions.ai/details/publication/pub.1085566283
35 https://doi.org/10.1007/bf00333132
36 schema:sdDatePublished 2022-09-02T15:45
37 schema:sdLicense https://scigraph.springernature.com/explorer/license/
38 schema:sdPublisher N980e64258585452da80171401550be62
39 schema:url https://doi.org/10.1007/bf00333132
40 sgo:license sg:explorer/license/
41 sgo:sdDataset articles
42 rdf:type schema:ScholarlyArticle
43 N41a0cca4336d436ca80a770b5396316c rdf:first sg:person.011520224512.05
44 rdf:rest N8f7841d3c5d543d7951dc37d0c716bc8
45 N4c7746291b564aaca05c0c77cec792b7 schema:volumeNumber 2
46 rdf:type schema:PublicationVolume
47 N818bd132b9244ae4a8084e4d89dae416 schema:name doi
48 schema:value 10.1007/bf00333132
49 rdf:type schema:PropertyValue
50 N87f7d87236c44074b7b5603bd81b6d21 rdf:first sg:person.015760032537.47
51 rdf:rest N41a0cca4336d436ca80a770b5396316c
52 N8f7841d3c5d543d7951dc37d0c716bc8 rdf:first sg:person.0727564714.69
53 rdf:rest rdf:nil
54 N980e64258585452da80171401550be62 schema:name Springer Nature - SN SciGraph project
55 rdf:type schema:Organization
56 Ne3366a5779a54ae8856d9911f57ad34b schema:issueNumber 3
57 rdf:type schema:PublicationIssue
58 Nf2f8831a35a14edea4795b3c2b29c9ff schema:name dimensions_id
59 schema:value pub.1085566283
60 rdf:type schema:PropertyValue
61 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
62 schema:name Mathematical Sciences
63 rdf:type schema:DefinedTerm
64 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
65 schema:name Pure Mathematics
66 rdf:type schema:DefinedTerm
67 sg:journal.1136683 schema:issn 0167-8094
68 1572-9273
69 schema:name Order
70 schema:publisher Springer Nature
71 rdf:type schema:Periodical
72 sg:person.011520224512.05 schema:affiliation grid-institutes:grid.432790.b
73 schema:familyName Saks
74 schema:givenName Michael
75 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011520224512.05
76 rdf:type schema:Person
77 sg:person.015760032537.47 schema:affiliation grid-institutes:grid.9619.7
78 schema:familyName Linial
79 schema:givenName Nathan
80 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015760032537.47
81 rdf:type schema:Person
82 sg:person.0727564714.69 schema:affiliation grid-institutes:grid.116068.8
83 schema:familyName Shor
84 schema:givenName Peter
85 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0727564714.69
86 rdf:type schema:Person
87 grid-institutes:grid.116068.8 schema:alternateName Department of Mathematics, MIT, 02139, Cambridge, MA, USA
88 schema:name Department of Mathematics, MIT, 02139, Cambridge, MA, USA
89 rdf:type schema:Organization
90 grid-institutes:grid.432790.b schema:alternateName Bell Communications Research, 435 South St., 07960, Morristown, NJ, USA
91 schema:name Bell Communications Research, 435 South St., 07960, Morristown, NJ, USA
92 rdf:type schema:Organization
93 grid-institutes:grid.9619.7 schema:alternateName Department of Computer Science, Hebrew University, Jerusalem, Israel
94 schema:name Department of Computer Science, Hebrew University, Jerusalem, Israel
95 rdf:type schema:Organization
 




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


...