{"id":"https://openalex.org/W4404413616","doi":"https://doi.org/10.37236/12312","title":"Non-Standard Binary Representations and the Stern Sequence","display_name":"Non-Standard Binary Representations and the Stern Sequence","publication_year":2024,"publication_date":"2024-11-15","ids":{"openalex":"https://openalex.org/W4404413616","doi":"https://doi.org/10.37236/12312"},"language":"en","primary_location":{"id":"doi:10.37236/12312","is_oa":true,"landing_page_url":"https://doi.org/10.37236/12312","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v31i4p39/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":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v31i4p39/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013180651","display_name":"Katie Anders","orcid":null},"institutions":[{"id":"https://openalex.org/I221716585","display_name":"The University of Texas at Tyler","ror":"https://ror.org/01azfw069","country_code":"US","type":"education","lineage":["https://openalex.org/I221716585"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Katie Anders","raw_affiliation_strings":["University of Texas at Tyler"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Texas at Tyler","institution_ids":["https://openalex.org/I221716585"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017660310","display_name":"Madeline Locus Dawsey","orcid":null},"institutions":[{"id":"https://openalex.org/I221716585","display_name":"The University of Texas at Tyler","ror":"https://ror.org/01azfw069","country_code":"US","type":"education","lineage":["https://openalex.org/I221716585"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Madeline Locus Dawsey","raw_affiliation_strings":["University of Texas at Tyler"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Texas at Tyler","institution_ids":["https://openalex.org/I221716585"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076477100","display_name":"Rajat Gupta","orcid":"https://orcid.org/0000-0002-3612-0034"},"institutions":[{"id":"https://openalex.org/I7947594","display_name":"University of Maine","ror":"https://ror.org/01adr0w49","country_code":"US","type":"education","lineage":["https://openalex.org/I2802397601","https://openalex.org/I7947594"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rajat Gupta","raw_affiliation_strings":["University of Maine"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Maine","institution_ids":["https://openalex.org/I7947594"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053212528","display_name":"Joseph Vandehey","orcid":null},"institutions":[{"id":"https://openalex.org/I221716585","display_name":"The University of Texas at Tyler","ror":"https://ror.org/01azfw069","country_code":"US","type":"education","lineage":["https://openalex.org/I221716585"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Joseph Vandehey","raw_affiliation_strings":["University of Texas at Tyler"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Texas at Tyler","institution_ids":["https://openalex.org/I221716585"]}]}],"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":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0895853,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"31","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11419","display_name":"Supramolecular Self-Assembly in Materials","score":0.9839000105857849,"subfield":{"id":"https://openalex.org/subfields/2502","display_name":"Biomaterials"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11419","display_name":"Supramolecular Self-Assembly in Materials","score":0.9839000105857849,"subfield":{"id":"https://openalex.org/subfields/2502","display_name":"Biomaterials"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/stern","display_name":"Stern","score":0.6771717667579651},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.6744413375854492},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.4892416000366211},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4076937735080719},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.37574630975723267},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.33608734607696533},{"id":"https://openalex.org/keywords/history","display_name":"History","score":0.1967642605304718},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.13572824001312256},{"id":"https://openalex.org/keywords/genetics","display_name":"Genetics","score":0.1331806480884552}],"concepts":[{"id":"https://openalex.org/C96597354","wikidata":"https://www.wikidata.org/wiki/Q273062","display_name":"Stern","level":2,"score":0.6771717667579651},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6744413375854492},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4892416000366211},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4076937735080719},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.37574630975723267},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33608734607696533},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.1967642605304718},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.13572824001312256},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.1331806480884552},{"id":"https://openalex.org/C195244886","wikidata":"https://www.wikidata.org/wiki/Q41493","display_name":"Ancient history","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/12312","is_oa":true,"landing_page_url":"https://doi.org/10.37236/12312","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v31i4p39/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":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/12312","is_oa":true,"landing_page_url":"https://doi.org/10.37236/12312","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v31i4p39/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":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.44999998807907104,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"},{"score":0.41999998688697815,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4404413616.pdf","grobid_xml":"https://content.openalex.org/works/W4404413616.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2056431439","https://openalex.org/W2329164258","https://openalex.org/W2110701497","https://openalex.org/W4206908931","https://openalex.org/W2924624619","https://openalex.org/W2391245012","https://openalex.org/W2501259145","https://openalex.org/W4230880605","https://openalex.org/W4396915211"],"abstract_inverted_index":{"We":[0,35],"show":[1,37],"that":[2,38],"the":[3,17,21],"number":[4],"of":[5,10,47,53],"short":[6],"binary":[7,50],"signed-digit":[8,51],"representations":[9,52],"an":[11],"integer":[12],"$n$":[13],"is":[14],"equal":[15],"to":[16],"$n$-th":[18],"term":[19],"in":[20],"Stern":[22],"sequence.":[23],"Various":[24],"proofs":[25],"are":[26],"provided,":[27],"including":[28],"direct,":[29],"bijective,":[30],"and":[31],"generating":[32],"function":[33],"proofs.":[34],"also":[36],"this":[39],"result":[40],"can":[41],"be":[42],"derived":[43],"from":[44],"recent":[45],"work":[46],"Monroe":[48],"on":[49],"a":[54],"fixed":[55],"length.":[56]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}