{"id":"https://openalex.org/W1556806394","doi":"https://doi.org/10.1007/978-3-540-85912-3_13","title":"The Combinatorics of Differentiation","display_name":"The Combinatorics of Differentiation","publication_year":2008,"publication_date":"2008-09-11","ids":{"openalex":"https://openalex.org/W1556806394","doi":"https://doi.org/10.1007/978-3-540-85912-3_13","mag":"1556806394"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-540-85912-3_13","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-85912-3_13","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5034196648","display_name":"Anna Bertiger","orcid":"https://orcid.org/0000-0002-7094-909X"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]},{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Anna S. Bertiger","raw_affiliation_strings":["California Institute of Technology, Cornell University, \u00a0","California Institute of Technology, Cornell University,#TAB#"],"affiliations":[{"raw_affiliation_string":"California Institute of Technology, Cornell University, \u00a0","institution_ids":["https://openalex.org/I205783295"]},{"raw_affiliation_string":"California Institute of Technology, Cornell University,#TAB#","institution_ids":["https://openalex.org/I122411786","https://openalex.org/I205783295"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032497643","display_name":"Robert J. McEliece","orcid":null},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]},{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Robert J. McEliece","raw_affiliation_strings":["California Institute of Technology, Cornell University, \u00a0","California Institute of Technology, Cornell University,#TAB#"],"affiliations":[{"raw_affiliation_string":"California Institute of Technology, Cornell University, \u00a0","institution_ids":["https://openalex.org/I205783295"]},{"raw_affiliation_string":"California Institute of Technology, Cornell University,#TAB#","institution_ids":["https://openalex.org/I122411786","https://openalex.org/I205783295"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063498718","display_name":"Sarah L. Sweatlock","orcid":null},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]},{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sarah Sweatlock","raw_affiliation_strings":["California Institute of Technology, Cornell University, \u00a0","California Institute of Technology, Cornell University,#TAB#"],"affiliations":[{"raw_affiliation_string":"California Institute of Technology, Cornell University, \u00a0","institution_ids":["https://openalex.org/I205783295"]},{"raw_affiliation_string":"California Institute of Technology, Cornell University,#TAB#","institution_ids":["https://openalex.org/I122411786","https://openalex.org/I205783295"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5034196648"],"corresponding_institution_ids":["https://openalex.org/I122411786","https://openalex.org/I205783295"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.1001281,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"142","last_page":"152"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9973999857902527,"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"}},"topics":[{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9973999857902527,"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/T11567","display_name":"semigroups and automata theory","score":0.9959999918937683,"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/T11130","display_name":"Coding theory and cryptography","score":0.9882000088691711,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/combinatorics","display_name":"Combinatorics","score":0.7306357622146606},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.7150436639785767},{"id":"https://openalex.org/keywords/combinatorics-on-words","display_name":"Combinatorics on words","score":0.639419436454773},{"id":"https://openalex.org/keywords/generating-function","display_name":"Generating function","score":0.564065158367157},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5222940444946289},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5066200494766235},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4592658281326294},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4346192479133606},{"id":"https://openalex.org/keywords/enumerative-combinatorics","display_name":"Enumerative combinatorics","score":0.4341524839401245},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.12926244735717773}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7306357622146606},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.7150436639785767},{"id":"https://openalex.org/C164804908","wikidata":"https://www.wikidata.org/wiki/Q2985058","display_name":"Combinatorics on words","level":3,"score":0.639419436454773},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.564065158367157},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5222940444946289},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5066200494766235},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4592658281326294},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4346192479133606},{"id":"https://openalex.org/C112497148","wikidata":"https://www.wikidata.org/wiki/Q336787","display_name":"Enumerative combinatorics","level":2,"score":0.4341524839401245},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.12926244735717773},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/978-3-540-85912-3_13","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-85912-3_13","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:authors.library.caltech.edu:88704","is_oa":false,"landing_page_url":"https://resolver.caltech.edu/CaltechAUTHORS:20180809-133557549","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Book Section"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1605190445","https://openalex.org/W2585931673","https://openalex.org/W2752853835","https://openalex.org/W2914659449","https://openalex.org/W4229873822","https://openalex.org/W4254016710","https://openalex.org/W6697549010"],"related_works":["https://openalex.org/W2006638646","https://openalex.org/W4313445281","https://openalex.org/W2319871891","https://openalex.org/W2136284319","https://openalex.org/W4376890880","https://openalex.org/W4286751119","https://openalex.org/W3022815041","https://openalex.org/W1551177513","https://openalex.org/W2184347621","https://openalex.org/W3181569274"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
