{"id":"https://openalex.org/W2943245916","doi":"https://doi.org/10.3934/amc.2020022","title":"Algebraic dependence in generating functions and expansion complexity","display_name":"Algebraic dependence in generating functions and expansion complexity","publication_year":2019,"publication_date":"2019-09-12","ids":{"openalex":"https://openalex.org/W2943245916","doi":"https://doi.org/10.3934/amc.2020022","mag":"2943245916"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2020022","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2020022","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=e97635ee-2cab-4ea4-bb45-922d84263356","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.aimsciences.org/article/exportPdf?id=e97635ee-2cab-4ea4-bb45-922d84263356","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063691894","display_name":"Domingo G\u00f3mez\u2010P\u00e9rez","orcid":"https://orcid.org/0000-0002-5780-2165"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Domingo G\u00f3mez-P\u00e9rez","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5037793363","display_name":"L\u00e1szl\u00f3 M\u00e9rai","orcid":"https://orcid.org/0000-0002-0437-7855"},"institutions":[{"id":"https://openalex.org/I138211613","display_name":"Austrian Academy of Sciences","ror":"https://ror.org/03anc3s24","country_code":"AT","type":"government","lineage":["https://openalex.org/I138211613"]},{"id":"https://openalex.org/I4210158379","display_name":"Johann Radon Institute for Computational and Applied Mathematics","ror":"https://ror.org/05a94k872","country_code":"AT","type":"facility","lineage":["https://openalex.org/I138211613","https://openalex.org/I4210158379"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"L\u00e1szl\u00f3 M\u00e9rai","raw_affiliation_strings":["Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenberger Stra\u00dfe 69, A-4040 Linz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenberger Stra\u00dfe 69, A-4040 Linz, Austria","institution_ids":["https://openalex.org/I4210158379","https://openalex.org/I138211613"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.03651748,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"2","first_page":"307","last_page":"318"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":1.0,"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"}},{"id":"https://openalex.org/T10951","display_name":"Cryptographic Implementations and Security","score":0.9968000054359436,"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"}},{"id":"https://openalex.org/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/randomness","display_name":"Randomness","score":0.766728401184082},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6307053565979004},{"id":"https://openalex.org/keywords/gr\u00f6bner-basis","display_name":"Gr\u00f6bner basis","score":0.48201242089271545},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4715304970741272},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.4252954125404358},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4201153516769409},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35600775480270386},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09838461875915527}],"concepts":[{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.766728401184082},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6307053565979004},{"id":"https://openalex.org/C198082693","wikidata":"https://www.wikidata.org/wiki/Q1551631","display_name":"Gr\u00f6bner basis","level":3,"score":0.48201242089271545},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4715304970741272},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.4252954125404358},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4201153516769409},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35600775480270386},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09838461875915527},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3934/amc.2020022","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2020022","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=e97635ee-2cab-4ea4-bb45-922d84263356","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1905.01079","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1905.01079","pdf_url":"https://arxiv.org/pdf/1905.01079","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"mag:2943245916","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1905.01079v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1905.01079","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1905.01079","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.3934/amc.2020022","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2020022","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=e97635ee-2cab-4ea4-bb45-922d84263356","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2720927368","display_name":null,"funder_award_id":"I1751-N26","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G3670442467","display_name":null,"funder_award_id":"P 31762","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2971669121","https://openalex.org/W2166867623","https://openalex.org/W1486146792","https://openalex.org/W3125711786","https://openalex.org/W144800253","https://openalex.org/W2593695978","https://openalex.org/W2051580005","https://openalex.org/W2130918732","https://openalex.org/W3098762489","https://openalex.org/W2949853196","https://openalex.org/W2911968827","https://openalex.org/W2039415523","https://openalex.org/W2285275878","https://openalex.org/W1964234068","https://openalex.org/W2735463758","https://openalex.org/W313025420","https://openalex.org/W282194388","https://openalex.org/W2417052859","https://openalex.org/W2269650202","https://openalex.org/W2963623809"],"abstract_inverted_index":{"In":[0,40],"2012,":[1],"Diem":[2],"introduced":[3],"a":[4,16],"new":[5,36],"figure":[6],"of":[7,18,25,34,38,55,59,81],"merit":[8],"for":[9,23,29,72],"cryptographic":[10],"sequences":[11,31,82],"called":[12],"expansion":[13,26,51,70,79],"complexity.":[14],"Recently,":[15],"series":[17],"paper":[19],"has":[20],"been":[21],"published":[22],"analysis":[24],"complexity":[27,52,71,80],"and":[28],"testing":[30],"in":[32,53],"terms":[33,54],"this":[35,41,45],"measure":[37],"randomness.":[39],"paper,":[42],"we":[43,48,65,76],"continue":[44],"analysis.":[46],"First":[47],"study":[49,77],"the":[50,56,60,69,78,88],"Gr\u00f6bner":[57],"basis":[58],"underlying":[61],"polynomial":[62],"ideal.":[63],"Next,":[64],"prove":[66],"bounds":[67],"on":[68],"random":[73],"sequences.":[74],"Finally,":[75],"defined":[83],"by":[84],"differential":[85],"equations,":[86],"including":[87],"inversive":[89],"generator.":[90]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
