{"id":"https://openalex.org/W2132076410","doi":"https://doi.org/10.1155/2013/305926","title":"The Height of a Class in the Cohomology Ring of Polygon Spaces","display_name":"The Height of a Class in the Cohomology Ring of Polygon Spaces","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2132076410","doi":"https://doi.org/10.1155/2013/305926","mag":"2132076410"},"language":"en","primary_location":{"id":"doi:10.1155/2013/305926","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/305926","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2013/305926.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/ijmms/2013/305926.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070871309","display_name":"Yasuhiko Kamiyama","orcid":"https://orcid.org/0000-0002-3850-0030"},"institutions":[{"id":"https://openalex.org/I32915989","display_name":"University of the Ryukyus","ror":"https://ror.org/02z1n9q24","country_code":"JP","type":"education","lineage":["https://openalex.org/I32915989"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Yasuhiko Kamiyama","raw_affiliation_strings":["Department of Mathematics, University of the Ryukyus, Nishihara-Cho, Okinawa 903-0213, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of the Ryukyus, Nishihara-Cho, Okinawa 903-0213, Japan","institution_ids":["https://openalex.org/I32915989"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023192110","display_name":"Kazufumi Kimoto","orcid":null},"institutions":[{"id":"https://openalex.org/I32915989","display_name":"University of the Ryukyus","ror":"https://ror.org/02z1n9q24","country_code":"JP","type":"education","lineage":["https://openalex.org/I32915989"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Kazufumi Kimoto","raw_affiliation_strings":["Department of Mathematics, University of the Ryukyus, Nishihara-Cho, Okinawa 903-0213, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of the Ryukyus, Nishihara-Cho, Okinawa 903-0213, Japan","institution_ids":["https://openalex.org/I32915989"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5070871309"],"corresponding_institution_ids":["https://openalex.org/I32915989"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":1.7596,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.83525278,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"2013","issue":null,"first_page":"1","last_page":"7"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9271844625473022},{"id":"https://openalex.org/keywords/cohomology","display_name":"Cohomology","score":0.5866639018058777},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.5742467045783997},{"id":"https://openalex.org/keywords/isometry","display_name":"Isometry (Riemannian geometry)","score":0.5690436363220215},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5521185398101807},{"id":"https://openalex.org/keywords/cohomology-ring","display_name":"Cohomology ring","score":0.5423972606658936},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5272083878517151},{"id":"https://openalex.org/keywords/polygon","display_name":"Polygon (computer graphics)","score":0.5196129679679871},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.5168724060058594},{"id":"https://openalex.org/keywords/equivariant-cohomology","display_name":"Equivariant cohomology","score":0.5020146369934082},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.4805058240890503},{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.44322526454925537},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4005533456802368},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36124616861343384},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.36013251543045044}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9271844625473022},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.5866639018058777},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.5742467045783997},{"id":"https://openalex.org/C82457910","wikidata":"https://www.wikidata.org/wiki/Q740207","display_name":"Isometry (Riemannian geometry)","level":2,"score":0.5690436363220215},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5521185398101807},{"id":"https://openalex.org/C2779185822","wikidata":"https://www.wikidata.org/wiki/Q5141399","display_name":"Cohomology ring","level":4,"score":0.5423972606658936},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5272083878517151},{"id":"https://openalex.org/C190694206","wikidata":"https://www.wikidata.org/wiki/Q3276654","display_name":"Polygon (computer graphics)","level":3,"score":0.5196129679679871},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.5168724060058594},{"id":"https://openalex.org/C72738302","wikidata":"https://www.wikidata.org/wiki/Q5384738","display_name":"Equivariant cohomology","level":3,"score":0.5020146369934082},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.4805058240890503},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.44322526454925537},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4005533456802368},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36124616861343384},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36013251543045044},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2013/305926","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/305926","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2013/305926.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jijmms:305926","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/IJMMS/2013/305926.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:c9441b17442643f4994f3f6c8cf85804","is_oa":true,"landing_page_url":"https://doaj.org/article/c9441b17442643f4994f3f6c8cf85804","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences, Vol 2013 (2013)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2013/305926","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/305926","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2013/305926.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.6899999976158142,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2132076410.pdf","grobid_xml":"https://content.openalex.org/works/W2132076410.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W1520783297","https://openalex.org/W2047406013","https://openalex.org/W2048159974","https://openalex.org/W2163563956","https://openalex.org/W2238763115"],"related_works":["https://openalex.org/W2028618230","https://openalex.org/W2951416080","https://openalex.org/W3199908143","https://openalex.org/W2029131257","https://openalex.org/W2952501174","https://openalex.org/W2165985881","https://openalex.org/W2950850201","https://openalex.org/W4377300853","https://openalex.org/W1933456157","https://openalex.org/W2013173375"],"abstract_inverted_index":{"Let":[0],",":[1,16,24,30,40,51,55,58,59,74,75,80,87],"be":[2],"the":[3,25,64,77,90],"configuration":[4],"space":[5],"of":[6,68],"planar":[7],"-gons":[8],"having":[9],"side":[10],"lengths":[11],"1,":[12],".":[13,14,15,52,53,54],"1":[17,50],"and":[18,76],"modulo":[19],"isometry":[20],"group.":[21],"For":[22,85],"generic":[23,86],"cohomology":[26],"ring":[27],"*":[28,38],"(":[29,39],";":[31,41],"Z":[32,42,46],"2":[33,43,47],")":[34,44,62,93,97,103],"has":[35],"a":[36,69],"form":[37],"=":[45,99,105],"[(,":[48],"),":[49],"-1":[56],"]/I":[57],"where":[60],"(,":[61,92,96,102],"is":[63,81],"first":[65],"Stiefel-Whitney":[66],"class":[67],"certain":[70],"regular":[71],"2-cover":[72],":":[73],"ideal":[78],"I":[79],"in":[82],"general":[83],"big.":[84],"we":[88],"determine":[89],"number":[91],"such":[94],"that":[95],"(,)":[98],"0":[100],"but":[101],"(,)+1":[104],"0.":[106]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
