{"id":"https://openalex.org/W2117673653","doi":"https://doi.org/10.1109/tit.2010.2040942","title":"Improved Lower Bounds on Capacities of Symmetric 2D Constraints Using Rayleigh Quotients","display_name":"Improved Lower Bounds on Capacities of Symmetric 2D Constraints Using Rayleigh Quotients","publication_year":2010,"publication_date":"2010-03-24","ids":{"openalex":"https://openalex.org/W2117673653","doi":"https://doi.org/10.1109/tit.2010.2040942","mag":"2117673653"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2010.2040942","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2010.2040942","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","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/A5049549712","display_name":"Erez Louidor","orcid":null},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Erez Louidor","raw_affiliation_strings":["Department of Mathematics, University of British Columbia, Vancouver, BC, Canada","Dept. of Math., Univ. of British Columbia, Vancouver, BC, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of British Columbia, Vancouver, BC, Canada","institution_ids":["https://openalex.org/I141945490"]},{"raw_affiliation_string":"Dept. of Math., Univ. of British Columbia, Vancouver, BC, Canada","institution_ids":["https://openalex.org/I141945490"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113544364","display_name":"Brian Marcus","orcid":null},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Brian H. Marcus","raw_affiliation_strings":["Department of Mathematics, University of British Columbia, Vancouver, BC, Canada","Dept. of Math., Univ. of British Columbia, Vancouver, BC, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of British Columbia, Vancouver, BC, Canada","institution_ids":["https://openalex.org/I141945490"]},{"raw_affiliation_string":"Dept. of Math., Univ. of British Columbia, Vancouver, BC, Canada","institution_ids":["https://openalex.org/I141945490"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5049549712"],"corresponding_institution_ids":["https://openalex.org/I141945490"],"apc_list":null,"apc_paid":null,"fwci":2.3417,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.88654486,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"56","issue":"4","first_page":"1624","last_page":"1639"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9937999844551086,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9937999844551086,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9751999974250793,"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/T12923","display_name":"Digital Image Processing Techniques","score":0.974399983882904,"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/generalization","display_name":"Generalization","score":0.7967400550842285},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.6071268916130066},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5751012563705444},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4915708005428314},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.45030534267425537},{"id":"https://openalex.org/keywords/emphasis","display_name":"Emphasis (telecommunications)","score":0.4359613358974457},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4337385594844818},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4160262942314148},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3895057141780853},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3552568256855011},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.31394028663635254},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13976919651031494}],"concepts":[{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.7967400550842285},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.6071268916130066},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5751012563705444},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4915708005428314},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.45030534267425537},{"id":"https://openalex.org/C177454536","wikidata":"https://www.wikidata.org/wiki/Q578290","display_name":"Emphasis (telecommunications)","level":2,"score":0.4359613358974457},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4337385594844818},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4160262942314148},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3895057141780853},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3552568256855011},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31394028663635254},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13976919651031494},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2010.2040942","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2010.2040942","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W81972919","https://openalex.org/W391578156","https://openalex.org/W643075289","https://openalex.org/W1556443961","https://openalex.org/W1565611252","https://openalex.org/W1619263573","https://openalex.org/W1653035750","https://openalex.org/W1992378780","https://openalex.org/W2038888225","https://openalex.org/W2053015204","https://openalex.org/W2056819163","https://openalex.org/W2062821497","https://openalex.org/W2092704115","https://openalex.org/W2096486078","https://openalex.org/W2104557113","https://openalex.org/W2105353526","https://openalex.org/W2118614862","https://openalex.org/W2128497840","https://openalex.org/W2136890907","https://openalex.org/W2158305334","https://openalex.org/W2610857016","https://openalex.org/W2970563090","https://openalex.org/W4206252072","https://openalex.org/W4212964805","https://openalex.org/W6636319156"],"related_works":["https://openalex.org/W2055105357","https://openalex.org/W2153819599","https://openalex.org/W2255426644","https://openalex.org/W2072124641","https://openalex.org/W2167093538","https://openalex.org/W2018956713","https://openalex.org/W1971573522","https://openalex.org/W2081479354","https://openalex.org/W2166972143","https://openalex.org/W2113107605"],"abstract_inverted_index":{"<para":[0],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[1],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[2],"A":[3],"method":[4,30,36,72],"for":[5,73],"computing":[6,74],"lower":[7,49],"bounds":[8,50,76],"on":[9,51,77],"capacities":[10,52,91],"of":[11,34,37,53,88,92,95],"two-dimensional":[12],"(2D)":[13],"constraints":[14,55,84,97],"having":[15],"a":[16,32],"symmetric":[17],"presentation":[18],"in":[19],"either":[20],"the":[21,24,35,59,78],"horizontal":[22],"or":[23],"vertical":[25],"direction":[26],"is":[27,31,62],"presented.":[28],"The":[29],"generalization":[33],"Calkin":[38],"and":[39],"Wilf":[40],"(SIAM":[41],"<emphasis":[42],"emphasistype=\"italic\">J.":[43],"Discrete":[44],"Math.</emphasis>,":[45],"1998).":[46],"Previous":[47],"best":[48],"certain":[54],"are":[56,86,98],"improved":[57],"using":[58],"method.":[60],"It":[61],"also":[63],"shown":[64],"how":[65],"this":[66],"method,":[67],"as":[68,70],"well":[69],"their":[71],"upper":[75],"capacity,":[79],"can":[80],"be":[81],"applied":[82],"to":[83],"which":[85],"not":[87],"finite-type.":[89],"Additionally,":[90],"two":[93],"families":[94],"multidimensional":[96],"given":[99],"exactly.":[100],"</para>":[101]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
