Monomial ideals induced by permutations avoiding patterns View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-02

AUTHORS

Ajay Kumar, Chanchal Kumar

ABSTRACT

Let S (or T) be the set of permutations of [n]={1,…,n} avoiding 123 and 132 patterns (or avoiding 123, 132 and 213 patterns). The monomial ideals IS=⟨xσ=∏i=1nxiσ(i):σ∈S⟩ and IT=⟨xσ:σ∈T⟩ in the polynomial ring R=k[x1,…,xn] over a field k have many interesting properties. The Alexander dual IS[n] of IS with respect to n=(n,…,n) has the minimal cellular resolution supported on the order complex Δ(Σn) of a poset Σn. The Alexander dual IT[n] also has the minimal cellular resolution supported on the order complex Δ(Σ~n) of a poset Σ~n. The number of standard monomials of the Artinian quotient RIS[n] is given by the number of irreducible (or indecomposable) permutations of [n+1], while the number of standard monomials of the Artinian quotient RIT[n] is given by the number of permutations of [n+1] having no substring {l,l+1}. More... »

PAGES

10

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s12044-018-0453-9

DOI

http://dx.doi.org/10.1007/s12044-018-0453-9

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1110756037


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/2008/0601", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Biochemistry and Cell Biology", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/06", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Biological Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "DAV University", 
          "id": "https://www.grid.ac/institutes/grid.472261.4", 
          "name": [
            "DAV University, 144 012, Jalandhar, Punjab, India"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Kumar", 
        "givenName": "Ajay", 
        "id": "sg:person.012574700163.98", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012574700163.98"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Indian Institute of Science Education and Research Mohali", 
          "id": "https://www.grid.ac/institutes/grid.458435.b", 
          "name": [
            "IISER Mohali, Knowledge City, Sector 81, SAS Nagar, 140 306, Mohali, Punjab, India"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Kumar", 
        "givenName": "Chanchal", 
        "id": "sg:person.013550463667.71", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013550463667.71"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/s00454-002-2776-6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1003378326", 
          "https://doi.org/10.1007/s00454-002-2776-6"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00454-002-2776-6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1003378326", 
          "https://doi.org/10.1007/s00454-002-2776-6"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0195-6698(85)80052-4", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1013083808"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s12044-014-0164-9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1016337643", 
          "https://doi.org/10.1007/s12044-014-0164-9"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1006/jsco.1999.0290", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1032586822"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1515/crll.1998.083", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1039169640"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/s0002-9947-04-03547-0", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1041856100"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.4310/mrl.1998.v5.n1.a3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1072461866"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.4310/mrl.1999.v6.n5.a5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1072461976"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2019-02", 
    "datePublishedReg": "2019-02-01", 
    "description": "Let S (or T) be the set of permutations of [n]={1,\u2026,n} avoiding 123 and 132 patterns (or avoiding 123, 132 and 213 patterns). The monomial ideals IS=\u27e8x\u03c3=\u220fi=1nxi\u03c3(i):\u03c3\u2208S\u27e9 and IT=\u27e8x\u03c3:\u03c3\u2208T\u27e9 in the polynomial ring R=k[x1,\u2026,xn] over a field k have many interesting properties. The Alexander dual IS[n] of IS with respect to n=(n,\u2026,n) has the minimal cellular resolution supported on the order complex \u0394(\u03a3n) of a poset \u03a3n. The Alexander dual IT[n] also has the minimal cellular resolution supported on the order complex \u0394(\u03a3~n) of a poset \u03a3~n. The number of standard monomials of the Artinian quotient RIS[n] is given by the number of irreducible (or indecomposable) permutations of [n+1], while the number of standard monomials of the Artinian quotient RIT[n] is given by the number of permutations of [n+1] having no substring {l,l+1}.", 
    "genre": "non_research_article", 
    "id": "sg:pub.10.1007/s12044-018-0453-9", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1320093", 
        "issn": [
          "2008-1359", 
          "2251-7456"
        ], 
        "name": "Proceedings - Mathematical Sciences", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "1", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "129"
      }
    ], 
    "name": "Monomial ideals induced by permutations avoiding patterns", 
    "pagination": "10", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "d5872377cfc29a77da030d6c727afba574ee6f6c9aac9c8eaba232f42e791a4c"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s12044-018-0453-9"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1110756037"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s12044-018-0453-9", 
      "https://app.dimensions.ai/details/publication/pub.1110756037"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T08:25", 
    "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/v90/0000000298_0000000298/records_26502_00000000.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://link.springer.com/10.1007%2Fs12044-018-0453-9"
  }
]
 

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/s12044-018-0453-9'

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/s12044-018-0453-9'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s12044-018-0453-9'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s12044-018-0453-9'


 

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

97 TRIPLES      21 PREDICATES      35 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s12044-018-0453-9 schema:about anzsrc-for:06
2 anzsrc-for:0601
3 schema:author Na0e75e9d354c41eb98a5d55152ec9ab8
4 schema:citation sg:pub.10.1007/s00454-002-2776-6
5 sg:pub.10.1007/s12044-014-0164-9
6 https://doi.org/10.1006/jsco.1999.0290
7 https://doi.org/10.1016/s0195-6698(85)80052-4
8 https://doi.org/10.1090/s0002-9947-04-03547-0
9 https://doi.org/10.1515/crll.1998.083
10 https://doi.org/10.4310/mrl.1998.v5.n1.a3
11 https://doi.org/10.4310/mrl.1999.v6.n5.a5
12 schema:datePublished 2019-02
13 schema:datePublishedReg 2019-02-01
14 schema:description Let S (or T) be the set of permutations of [n]={1,…,n} avoiding 123 and 132 patterns (or avoiding 123, 132 and 213 patterns). The monomial ideals IS=⟨xσ=∏i=1nxiσ(i):σ∈S⟩ and IT=⟨xσ:σ∈T⟩ in the polynomial ring R=k[x1,…,xn] over a field k have many interesting properties. The Alexander dual IS[n] of IS with respect to n=(n,…,n) has the minimal cellular resolution supported on the order complex Δ(Σn) of a poset Σn. The Alexander dual IT[n] also has the minimal cellular resolution supported on the order complex Δ(Σ~n) of a poset Σ~n. The number of standard monomials of the Artinian quotient RIS[n] is given by the number of irreducible (or indecomposable) permutations of [n+1], while the number of standard monomials of the Artinian quotient RIT[n] is given by the number of permutations of [n+1] having no substring {l,l+1}.
15 schema:genre non_research_article
16 schema:inLanguage en
17 schema:isAccessibleForFree false
18 schema:isPartOf N8d4b87b2f6854e8fb66228e7e884805a
19 Ne46f73ef7acb493e83b4e5d6d0ee8ac8
20 sg:journal.1320093
21 schema:name Monomial ideals induced by permutations avoiding patterns
22 schema:pagination 10
23 schema:productId Nbe6527c338554fa6912bb19a7145f026
24 Nf6f4f2d56bfb47a4824e4271234485a5
25 Nf9ab9d08481b42efb2b4217131276f0a
26 schema:sameAs https://app.dimensions.ai/details/publication/pub.1110756037
27 https://doi.org/10.1007/s12044-018-0453-9
28 schema:sdDatePublished 2019-04-11T08:25
29 schema:sdLicense https://scigraph.springernature.com/explorer/license/
30 schema:sdPublisher Ndefe78a524a54bc58819056c75a62997
31 schema:url https://link.springer.com/10.1007%2Fs12044-018-0453-9
32 sgo:license sg:explorer/license/
33 sgo:sdDataset articles
34 rdf:type schema:ScholarlyArticle
35 N1ee7ce92d113401a873a34304cc04d27 rdf:first sg:person.013550463667.71
36 rdf:rest rdf:nil
37 N8d4b87b2f6854e8fb66228e7e884805a schema:volumeNumber 129
38 rdf:type schema:PublicationVolume
39 Na0e75e9d354c41eb98a5d55152ec9ab8 rdf:first sg:person.012574700163.98
40 rdf:rest N1ee7ce92d113401a873a34304cc04d27
41 Nbe6527c338554fa6912bb19a7145f026 schema:name readcube_id
42 schema:value d5872377cfc29a77da030d6c727afba574ee6f6c9aac9c8eaba232f42e791a4c
43 rdf:type schema:PropertyValue
44 Ndefe78a524a54bc58819056c75a62997 schema:name Springer Nature - SN SciGraph project
45 rdf:type schema:Organization
46 Ne46f73ef7acb493e83b4e5d6d0ee8ac8 schema:issueNumber 1
47 rdf:type schema:PublicationIssue
48 Nf6f4f2d56bfb47a4824e4271234485a5 schema:name dimensions_id
49 schema:value pub.1110756037
50 rdf:type schema:PropertyValue
51 Nf9ab9d08481b42efb2b4217131276f0a schema:name doi
52 schema:value 10.1007/s12044-018-0453-9
53 rdf:type schema:PropertyValue
54 anzsrc-for:06 schema:inDefinedTermSet anzsrc-for:
55 schema:name Biological Sciences
56 rdf:type schema:DefinedTerm
57 anzsrc-for:0601 schema:inDefinedTermSet anzsrc-for:
58 schema:name Biochemistry and Cell Biology
59 rdf:type schema:DefinedTerm
60 sg:journal.1320093 schema:issn 2008-1359
61 2251-7456
62 schema:name Proceedings - Mathematical Sciences
63 rdf:type schema:Periodical
64 sg:person.012574700163.98 schema:affiliation https://www.grid.ac/institutes/grid.472261.4
65 schema:familyName Kumar
66 schema:givenName Ajay
67 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012574700163.98
68 rdf:type schema:Person
69 sg:person.013550463667.71 schema:affiliation https://www.grid.ac/institutes/grid.458435.b
70 schema:familyName Kumar
71 schema:givenName Chanchal
72 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013550463667.71
73 rdf:type schema:Person
74 sg:pub.10.1007/s00454-002-2776-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003378326
75 https://doi.org/10.1007/s00454-002-2776-6
76 rdf:type schema:CreativeWork
77 sg:pub.10.1007/s12044-014-0164-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016337643
78 https://doi.org/10.1007/s12044-014-0164-9
79 rdf:type schema:CreativeWork
80 https://doi.org/10.1006/jsco.1999.0290 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032586822
81 rdf:type schema:CreativeWork
82 https://doi.org/10.1016/s0195-6698(85)80052-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1013083808
83 rdf:type schema:CreativeWork
84 https://doi.org/10.1090/s0002-9947-04-03547-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1041856100
85 rdf:type schema:CreativeWork
86 https://doi.org/10.1515/crll.1998.083 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039169640
87 rdf:type schema:CreativeWork
88 https://doi.org/10.4310/mrl.1998.v5.n1.a3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072461866
89 rdf:type schema:CreativeWork
90 https://doi.org/10.4310/mrl.1999.v6.n5.a5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072461976
91 rdf:type schema:CreativeWork
92 https://www.grid.ac/institutes/grid.458435.b schema:alternateName Indian Institute of Science Education and Research Mohali
93 schema:name IISER Mohali, Knowledge City, Sector 81, SAS Nagar, 140 306, Mohali, Punjab, India
94 rdf:type schema:Organization
95 https://www.grid.ac/institutes/grid.472261.4 schema:alternateName DAV University
96 schema:name DAV University, 144 012, Jalandhar, Punjab, India
97 rdf:type schema:Organization
 




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


...