{"id":"https://openalex.org/W2983249467","doi":"https://doi.org/10.1007/s11786-019-00421-8","title":"The Depth of Compositions","display_name":"The Depth of Compositions","publication_year":2019,"publication_date":"2019-11-13","ids":{"openalex":"https://openalex.org/W2983249467","doi":"https://doi.org/10.1007/s11786-019-00421-8","mag":"2983249467"},"language":"en","primary_location":{"id":"doi:10.1007/s11786-019-00421-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11786-019-00421-8","pdf_url":null,"source":{"id":"https://openalex.org/S136038430","display_name":"Mathematics in Computer Science","issn_l":"1661-8270","issn":["1661-8270","1661-8289"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069087150","display_name":"Aubrey Blecher","orcid":"https://orcid.org/0000-0003-2487-3220"},"institutions":[{"id":"https://openalex.org/I192619145","display_name":"University of the Witwatersrand","ror":"https://ror.org/03rp50x72","country_code":"ZA","type":"education","lineage":["https://openalex.org/I192619145"]}],"countries":["ZA"],"is_corresponding":false,"raw_author_name":"Aubrey Blecher","raw_affiliation_strings":["The John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits, Johannesburg, 2050, South Africa","The John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand, Johannesburg, South Africa"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits, Johannesburg, 2050, South Africa","institution_ids":["https://openalex.org/I192619145"]},{"raw_affiliation_string":"The John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand, Johannesburg, South Africa","institution_ids":["https://openalex.org/I192619145"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091781778","display_name":"Charlotte Brennan","orcid":"https://orcid.org/0000-0002-9980-9744"},"institutions":[{"id":"https://openalex.org/I192619145","display_name":"University of the Witwatersrand","ror":"https://ror.org/03rp50x72","country_code":"ZA","type":"education","lineage":["https://openalex.org/I192619145"]}],"countries":["ZA"],"is_corresponding":true,"raw_author_name":"Charlotte Brennan","raw_affiliation_strings":["The John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits, Johannesburg, 2050, South Africa","The John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand, Johannesburg, South Africa"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits, Johannesburg, 2050, South Africa","institution_ids":["https://openalex.org/I192619145"]},{"raw_affiliation_string":"The John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand, Johannesburg, South Africa","institution_ids":["https://openalex.org/I192619145"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036711367","display_name":"Arnold Knopfmacher","orcid":"https://orcid.org/0000-0003-1962-043X"},"institutions":[{"id":"https://openalex.org/I192619145","display_name":"University of the Witwatersrand","ror":"https://ror.org/03rp50x72","country_code":"ZA","type":"education","lineage":["https://openalex.org/I192619145"]}],"countries":["ZA"],"is_corresponding":false,"raw_author_name":"Arnold Knopfmacher","raw_affiliation_strings":["The John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits, Johannesburg, 2050, South Africa","The John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand, Johannesburg, South Africa"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits, Johannesburg, 2050, South Africa","institution_ids":["https://openalex.org/I192619145"]},{"raw_affiliation_string":"The John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand, Johannesburg, South Africa","institution_ids":["https://openalex.org/I192619145"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024416044","display_name":"Toufik Mansour","orcid":"https://orcid.org/0000-0001-8028-2391"},"institutions":[{"id":"https://openalex.org/I91203450","display_name":"University of Haifa","ror":"https://ror.org/02f009v59","country_code":"IL","type":"education","lineage":["https://openalex.org/I91203450"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Toufik Mansour","raw_affiliation_strings":["Department of Mathematics, University of Haifa, 3498838, Haifa, Israel","Department of Mathematics, University of Haifa, Haifa, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Haifa, 3498838, Haifa, Israel","institution_ids":["https://openalex.org/I91203450"]},{"raw_affiliation_string":"Department of Mathematics, University of Haifa, Haifa, Israel","institution_ids":["https://openalex.org/I91203450"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5091781778"],"corresponding_institution_ids":["https://openalex.org/I192619145"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.2929257,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"1","first_page":"69","last_page":"76"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9997000098228455,"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":0.9997000098228455,"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/T11567","display_name":"semigroups and automata theory","score":0.9916999936103821,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9915000200271606,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/composition","display_name":"Composition (language)","score":0.7016162276268005},{"id":"https://openalex.org/keywords/unit","display_name":"Unit (ring theory)","score":0.5809230804443359},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5555569529533386},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5152945518493652},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4422934949398041},{"id":"https://openalex.org/keywords/component","display_name":"Component (thermodynamics)","score":0.4287399649620056},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12362122535705566}],"concepts":[{"id":"https://openalex.org/C40231798","wikidata":"https://www.wikidata.org/wiki/Q1333743","display_name":"Composition (language)","level":2,"score":0.7016162276268005},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.5809230804443359},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5555569529533386},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5152945518493652},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4422934949398041},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.4287399649620056},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12362122535705566},{"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11786-019-00421-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11786-019-00421-8","pdf_url":null,"source":{"id":"https://openalex.org/S136038430","display_name":"Mathematics in Computer Science","issn_l":"1661-8270","issn":["1661-8270","1661-8289"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics in Computer Science","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/13","display_name":"Climate action","score":0.41999998688697815}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W17399337","https://openalex.org/W1491178396","https://openalex.org/W2002089154","https://openalex.org/W2003250112","https://openalex.org/W2008819031","https://openalex.org/W2013073424","https://openalex.org/W2016514341","https://openalex.org/W2025773144","https://openalex.org/W2909570313","https://openalex.org/W2910947730","https://openalex.org/W2993394850","https://openalex.org/W3105746648","https://openalex.org/W4302339081"],"related_works":["https://openalex.org/W2357256365","https://openalex.org/W2348502264","https://openalex.org/W611386996","https://openalex.org/W2365486383","https://openalex.org/W2362059367","https://openalex.org/W1499958165","https://openalex.org/W2901443725","https://openalex.org/W2350084742","https://openalex.org/W2380193321","https://openalex.org/W2352623374"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}