{"id":"https://openalex.org/W2102196430","doi":"https://doi.org/10.37236/1498","title":"Composition sum identities related to the distribution of coordinate values in a discrete simplex","display_name":"Composition sum identities related to the distribution of coordinate values in a discrete simplex","publication_year":2000,"publication_date":"2000-04-13","ids":{"openalex":"https://openalex.org/W2102196430","doi":"https://doi.org/10.37236/1498","mag":"2102196430"},"language":"en","primary_location":{"id":"doi:10.37236/1498","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1498","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v7i1r20/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v7i1r20/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028119802","display_name":"Robert Milson","orcid":"https://orcid.org/0000-0002-2868-7866"},"institutions":[{"id":"https://openalex.org/I129902397","display_name":"Dalhousie University","ror":"https://ror.org/01e6qks80","country_code":"CA","type":"education","lineage":["https://openalex.org/I129902397"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"R. Milson","raw_affiliation_strings":["DALHOUSIE UNIVERSITY HALIFAX, N.S. B3H 3J5 CANADA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DALHOUSIE UNIVERSITY HALIFAX, N.S. B3H 3J5 CANADA","institution_ids":["https://openalex.org/I129902397"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5028119802"],"corresponding_institution_ids":["https://openalex.org/I129902397"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.17149666,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"7","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9901999831199646,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9901999831199646,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9871000051498413,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.980400025844574,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.8772488832473755},{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.7443835139274597},{"id":"https://openalex.org/keywords/simplex","display_name":"Simplex","score":0.6962227821350098},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6599339842796326},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.5720353126525879},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5118510127067566},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4863910973072052},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4792173504829407},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.46882861852645874},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.443711519241333},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4368031620979309},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.41557133197784424},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4004262685775757},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11986187100410461}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8772488832473755},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.7443835139274597},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.6962227821350098},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6599339842796326},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.5720353126525879},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5118510127067566},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4863910973072052},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4792173504829407},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.46882861852645874},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.443711519241333},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4368031620979309},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.41557133197784424},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4004262685775757},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11986187100410461},{"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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/1498","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1498","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v7i1r20/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.236.9492","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.236.9492","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0003126v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.85.6685","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.85.6685","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.emis.de/journals/EJC/Volume_7/PDF/v7i1r20.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1498","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1498","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v7i1r20/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2102196430.pdf","grobid_xml":"https://content.openalex.org/works/W2102196430.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1642476103","https://openalex.org/W1990673358","https://openalex.org/W2128817474","https://openalex.org/W2795955538","https://openalex.org/W2911361414","https://openalex.org/W3145991194","https://openalex.org/W4237376241","https://openalex.org/W4285719527","https://openalex.org/W4291474784"],"related_works":["https://openalex.org/W2952259524","https://openalex.org/W2279732055","https://openalex.org/W2051058708","https://openalex.org/W2995857455","https://openalex.org/W4288805235","https://openalex.org/W2998840281","https://openalex.org/W2027277382","https://openalex.org/W4287020903","https://openalex.org/W1552538164","https://openalex.org/W2982781090"],"abstract_inverted_index":{"Utilizing":[0],"spectral":[1],"residues":[2],"of":[3,16,28,30,50,54,71,74,91,114,120,132],"parameterized,":[4],"recursively":[5],"defined":[6],"sequences,":[7],"we":[8,109],"develop":[9],"a":[10,48,98,115],"general":[11],"method":[12],"for":[13],"generating":[14],"identities":[15,45,58],"composition":[17],"sums.":[18],"Specific":[19],"results":[20],"are":[21],"obtained":[22],"by":[23,136,140],"focusing":[24],"on":[25],"coefficient":[26],"sequences":[27],"solutions":[29],"first":[31,41],"and":[32,126],"second":[33,61],"order,":[34],"ordinary,":[35],"linear":[36],"differential":[37],"equations.":[38],"Regarding":[39],"the":[40,43,51,60,72,85,88,104,123,130],"class,":[42],"corresponding":[44],"amount":[46],"to":[47,66,129],"proof":[49,113],"exponential":[52],"formula":[53],"labelled":[55],"counting.":[56],"The":[57],"in":[59,97,122],"class":[62],"can":[63],"be":[64],"used":[65],"establish":[67],"certain":[68,99],"geometric":[69],"properties":[70],"simplex":[73,95],"bounded,":[75],"ordered,":[76],"integer":[77],"tuples.":[78],"We":[79],"present":[80],"three":[81],"theorems":[82],"that":[83,87],"support":[84],"conclusion":[86],"inner":[89],"dimensions":[90],"such":[92],"an":[93,111],"order":[94,124],"are,":[96],"sense,":[100],"more":[101],"ample":[102],"than":[103,139],"outer":[105],"dimensions.":[106],"As":[107],"well,":[108],"give":[110],"algebraic":[112,141],"bijection":[116,135],"between":[117],"two":[118],"families":[119],"subsets":[121],"simplex,":[125],"inquire":[127],"as":[128],"possibility":[131],"establishing":[133],"this":[134],"combinatorial,":[137],"rather":[138],"methods.":[142]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}