{"id":"https://openalex.org/W2102935164","doi":null,"title":"Some Useful Properties of Composition","display_name":"Some Useful Properties of Composition","publication_year":1962,"publication_date":"1962-03-01","ids":{"openalex":"https://openalex.org/W2102935164","mag":"2102935164"},"language":"en","primary_location":{"id":"pmh:oai:www.ideals.illinois.edu:2142/73984","doi":null,"is_oa":true,"landing_page_url":"https://hdl.handle.net/2142/73984","pdf_url":"https://www.ideals.illinois.edu/items/99992/bitstreams/319454/data.pdf","source":{"id":"https://openalex.org/S4306401358","display_name":"Illinois Digital Environment for Access to Learning and Scholarship (University of Illinois at Urbana-Champaign)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I2801919071","host_organization_name":"University of Illinois System","host_organization_lineage":["https://openalex.org/I2801919071"],"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":"text"},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.ideals.illinois.edu/items/99992/bitstreams/319454/data.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108439542","display_name":"Basil R. Myers","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"B.R. Myers","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5108439542"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.25701944,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.0007999999797903001,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.0005000000237487257,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/integer-compositions","display_name":"integer compositions","score":0.7549999952316284},{"id":"https://openalex.org/keywords/matrix-representation","display_name":"matrix representation","score":0.7699999809265137},{"id":"https://openalex.org/keywords/sequencing-problems","display_name":"sequencing problems","score":0.8640000224113464},{"id":"https://openalex.org/keywords/combinatorial-properties","display_name":"combinatorial properties","score":0.7799999713897705}],"concepts":[{"id":"https://openalex.org/C40231798","wikidata":"https://www.wikidata.org/wiki/Q1333743","display_name":"Composition (language)","level":2,"score":0.6534686088562012},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.621958315372467},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5020496845245361},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.463555246591568},{"id":"https://openalex.org/C103275481","wikidata":"https://www.wikidata.org/wiki/Q6787889","display_name":"Matrix representation","level":3,"score":0.4370030462741852},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3654715120792389},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36005210876464844},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3521019220352173},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.23966029286384583},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.10830852389335632},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.08605170249938965},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.06155449151992798},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.054694801568984985},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","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/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:www.ideals.illinois.edu:2142/73984","doi":null,"is_oa":true,"landing_page_url":"https://hdl.handle.net/2142/73984","pdf_url":"https://www.ideals.illinois.edu/items/99992/bitstreams/319454/data.pdf","source":{"id":"https://openalex.org/S4306401358","display_name":"Illinois Digital Environment for Access to Learning and Scholarship (University of Illinois at Urbana-Champaign)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I2801919071","host_organization_name":"University of Illinois System","host_organization_lineage":["https://openalex.org/I2801919071"],"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":"text"},{"id":"pmh:AD0275582","doi":null,"is_oa":false,"landing_page_url":"http://oai.dtic.mil/oai/oai?&amp;verb=getRecord&amp;metadataPrefix=html&amp;identifier=AD0275582","pdf_url":null,"source":{"id":"https://openalex.org/S4406923043","display_name":"Defense Technical Information Center (DTIC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"DTIC AND NTIS","raw_type":"Text"},{"id":"mag:2102935164","doi":null,"is_oa":false,"landing_page_url":"https://www.ideals.illinois.edu/handle/2142/73984","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:www.ideals.illinois.edu:2142/73984","doi":null,"is_oa":true,"landing_page_url":"https://hdl.handle.net/2142/73984","pdf_url":"https://www.ideals.illinois.edu/items/99992/bitstreams/319454/data.pdf","source":{"id":"https://openalex.org/S4306401358","display_name":"Illinois Digital Environment for Access to Learning and Scholarship (University of Illinois at Urbana-Champaign)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I2801919071","host_organization_name":"University of Illinois System","host_organization_lineage":["https://openalex.org/I2801919071"],"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":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320332222","display_name":"University of Illinois at Urbana-Champaign","ror":"https://ror.org/047426m28"},{"id":"https://openalex.org/F4320332923","display_name":"U.S. Navy","ror":"https://ror.org/03ar0mv07"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2102935164.pdf","grobid_xml":"https://content.openalex.org/works/W2102935164.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2617348446","https://openalex.org/W1981356819","https://openalex.org/W3210160619","https://openalex.org/W4400208947","https://openalex.org/W7058241505","https://openalex.org/W4297804614","https://openalex.org/W2067950549","https://openalex.org/W7096362815","https://openalex.org/W152713790","https://openalex.org/W207210083"],"abstract_inverted_index":{"A":[0],"matrix":[1],"representation":[2],"of":[3,5,20,27,30,36],"compositions":[4],"the":[6,18,28,34],"positive":[7],"real":[8],"integers":[9],"leads":[10],"to":[11],"some":[12],"useful":[13],"lemmas":[14],"and":[15,22],"theorems":[16],"on":[17],"properties":[19,32],"single":[21],"multiple":[23],"compositions.Examples":[24],"are":[25],"given":[26],"application":[29],"these":[31],"in":[33],"analysis":[35],"sequencing":[37],"problems.":[38]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2016-06-24T00:00:00"}
