{"id":"https://openalex.org/W2612621433","doi":"https://doi.org/10.3934/amc.2017022","title":"Explicit formulas for monomial involutions over finite fields","display_name":"Explicit formulas for monomial involutions over finite fields","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2612621433","doi":"https://doi.org/10.3934/amc.2017022","mag":"2612621433"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2017022","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2017022","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.3934/amc.2017022","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110505253","display_name":"Francis N. Castro","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Francis N. Castro","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029180668","display_name":"Carlos J. Corrada-Bravo","orcid":null},"institutions":[{"id":"https://openalex.org/I1662191","display_name":"University of Puerto Rico at R\u00edo Piedras","ror":"https://ror.org/0453v4r20","country_code":"PR","type":"education","lineage":["https://openalex.org/I1662191","https://openalex.org/I200399037"]}],"countries":["PR"],"is_corresponding":false,"raw_author_name":"Carlos Corrada-Bravo","raw_affiliation_strings":["Department of Computer Science, University of Puerto Rico, R\u00edo Piedras, Box 70377, S.J., PR 00936-8377"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Puerto Rico, R\u00edo Piedras, Box 70377, S.J., PR 00936-8377","institution_ids":["https://openalex.org/I1662191"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056478164","display_name":"Natalia Pacheco-Tallaj","orcid":"https://orcid.org/0000-0003-1637-9492"},"institutions":[{"id":"https://openalex.org/I1662191","display_name":"University of Puerto Rico at R\u00edo Piedras","ror":"https://ror.org/0453v4r20","country_code":"PR","type":"education","lineage":["https://openalex.org/I1662191","https://openalex.org/I200399037"]}],"countries":["PR"],"is_corresponding":false,"raw_author_name":"Natalia Pacheco-Tallaj","raw_affiliation_strings":["Department of Computer Science, University of Puerto Rico, R\u00edo Piedras, Box 70377, S.J., PR 00936-8377"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Puerto Rico, R\u00edo Piedras, Box 70377, S.J., PR 00936-8377","institution_ids":["https://openalex.org/I1662191"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000623639","display_name":"Ivelisse Rubio","orcid":"https://orcid.org/0000-0001-5183-0256"},"institutions":[{"id":"https://openalex.org/I1662191","display_name":"University of Puerto Rico at R\u00edo Piedras","ror":"https://ror.org/0453v4r20","country_code":"PR","type":"education","lineage":["https://openalex.org/I1662191","https://openalex.org/I200399037"]}],"countries":["PR"],"is_corresponding":false,"raw_author_name":"Ivelisse Rubio","raw_affiliation_strings":["Department of Computer Science, University of Puerto Rico, R\u00edo Piedras, Box 70377, S.J., PR 00936-8377"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Puerto Rico, R\u00edo Piedras, Box 70377, S.J., PR 00936-8377","institution_ids":["https://openalex.org/I1662191"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5110505253"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8308,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.79960663,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"11","issue":"2","first_page":"301","last_page":"306"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9969000220298767,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9969000220298767,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9379634857177734},{"id":"https://openalex.org/keywords/monomial","display_name":"Monomial","score":0.8963943719863892},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.7112441062927246},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5193256139755249},{"id":"https://openalex.org/keywords/coding-theory","display_name":"Coding theory","score":0.5189414024353027},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.498978853225708},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.4678764045238495},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.44765931367874146},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3781643807888031},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3613606095314026},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1326574683189392},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.056060969829559326}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9379634857177734},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.8963943719863892},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.7112441062927246},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5193256139755249},{"id":"https://openalex.org/C113709454","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Coding theory","level":2,"score":0.5189414024353027},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.498978853225708},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.4678764045238495},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.44765931367874146},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3781643807888031},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3613606095314026},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1326574683189392},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.056060969829559326}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3934/amc.2017022","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2017022","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3934/amc.2017022","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2017022","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1525301310","https://openalex.org/W2100098924","https://openalex.org/W2113686932","https://openalex.org/W2301421650","https://openalex.org/W2392885651","https://openalex.org/W3100996381","https://openalex.org/W4285719527","https://openalex.org/W4299551152","https://openalex.org/W6636714939"],"related_works":["https://openalex.org/W373615522","https://openalex.org/W2768765413","https://openalex.org/W223331605","https://openalex.org/W1610556314","https://openalex.org/W2258715480","https://openalex.org/W1582299817","https://openalex.org/W2801596938","https://openalex.org/W2230283315","https://openalex.org/W4238916473","https://openalex.org/W2907080524"],"abstract_inverted_index":{"Permutations":[0],"of":[1,22,45],"finite":[2],"fields":[3],"have":[4],"important":[5],"applications":[6],"in":[7],"cryptography":[8],"and":[9,20,53],"coding":[10,30],"theory.":[11],"Involutions":[12],"are":[13,16,21,49],"permutations":[14],"that":[15,48],"its":[17],"own":[18],"inverse":[19],"particular":[23],"interest":[24],"because":[25],"the":[26,43],"implementation":[27],"used":[28,34],"for":[29,35,41,54],"can":[31],"also":[32],"be":[33],"decoding.":[36],"We":[37],"present":[38],"explicit":[39],"formulas":[40],"all":[42],"involutions":[44],"${\\mathbb{":[46],"F\\!}}_q$":[47],"given":[50],"by":[51],"monomials":[52],"their":[55],"fixed":[56],"points.":[57]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2026-03-25T13:04:00.132906","created_date":"2025-10-10T00:00:00"}