{"id":"https://openalex.org/W1829319199","doi":"https://doi.org/10.37236/3395","title":"Kauffman's Clock Lattice as a Graph of Perfect Matchings: a Formula for its Height","display_name":"Kauffman's Clock Lattice as a Graph of Perfect Matchings: a Formula for its Height","publication_year":2014,"publication_date":"2014-11-13","ids":{"openalex":"https://openalex.org/W1829319199","doi":"https://doi.org/10.37236/3395","mag":"1829319199"},"language":"en","primary_location":{"id":"doi:10.37236/3395","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3395","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v21i4p31/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/v21i4p31/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038573069","display_name":"Moshe Cohen","orcid":"https://orcid.org/0000-0003-0770-3131"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Moshe Cohen","raw_affiliation_strings":["Technion - Israel Institute of Technology","TECHNION-Israel Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technion - Israel Institute of Technology","institution_ids":["https://openalex.org/I174306211"]},{"raw_affiliation_string":"TECHNION-Israel Institute of Technology","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091766722","display_name":"Mina Teicher","orcid":"https://orcid.org/0000-0003-1700-9709"},"institutions":[{"id":"https://openalex.org/I13955877","display_name":"Bar-Ilan University","ror":"https://ror.org/03kgsv495","country_code":"IL","type":"education","lineage":["https://openalex.org/I13955877"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Mina Teicher","raw_affiliation_strings":["Bar-Ilan University","Bar Ilan University ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bar-Ilan University","institution_ids":["https://openalex.org/I13955877"]},{"raw_affiliation_string":"Bar Ilan University ,","institution_ids":["https://openalex.org/I13955877"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3743,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.77713987,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"21","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9921000003814697,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.978600025177002,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8099819421768188},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.7259122729301453},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6785039901733398},{"id":"https://openalex.org/keywords/lattice-graph","display_name":"Lattice graph","score":0.6164718866348267},{"id":"https://openalex.org/keywords/crossing-number","display_name":"Crossing number (knot theory)","score":0.49458763003349304},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.483851820230484},{"id":"https://openalex.org/keywords/complete-bipartite-graph","display_name":"Complete bipartite graph","score":0.4461749196052551},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.44508761167526245},{"id":"https://openalex.org/keywords/knot","display_name":"Knot (papermaking)","score":0.44165512919425964},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3873385787010193},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.3590158224105835}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8099819421768188},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.7259122729301453},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6785039901733398},{"id":"https://openalex.org/C145580432","wikidata":"https://www.wikidata.org/wiki/Q6497118","display_name":"Lattice graph","level":5,"score":0.6164718866348267},{"id":"https://openalex.org/C2777724877","wikidata":"https://www.wikidata.org/wiki/Q2548661","display_name":"Crossing number (knot theory)","level":3,"score":0.49458763003349304},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.483851820230484},{"id":"https://openalex.org/C134119311","wikidata":"https://www.wikidata.org/wiki/Q913598","display_name":"Complete bipartite graph","level":4,"score":0.4461749196052551},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.44508761167526245},{"id":"https://openalex.org/C2779863119","wikidata":"https://www.wikidata.org/wiki/Q6423048","display_name":"Knot (papermaking)","level":2,"score":0.44165512919425964},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3873385787010193},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.3590158224105835},{"id":"https://openalex.org/C42360764","wikidata":"https://www.wikidata.org/wiki/Q83588","display_name":"Chemical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/3395","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3395","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v21i4p31/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:10.37236/3395","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3395","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v21i4p31/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":[{"id":"https://metadata.un.org/sdg/11","score":0.5299999713897705,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320310395","display_name":"Louisiana State University","ror":"https://ror.org/05ect4e57"},{"id":"https://openalex.org/F4320320878","display_name":"Minerva Foundation","ror":"https://ror.org/02rxjts25"},{"id":"https://openalex.org/F4320321449","display_name":"Bar-Ilan University","ror":"https://ror.org/03kgsv495"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1829319199.pdf","grobid_xml":"https://content.openalex.org/works/W1829319199.grobid-xml"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W140130170","https://openalex.org/W564413792","https://openalex.org/W1488663833","https://openalex.org/W1540312541","https://openalex.org/W1563331286","https://openalex.org/W1569752386","https://openalex.org/W1963675492","https://openalex.org/W1974398302","https://openalex.org/W1985383247","https://openalex.org/W1987640305","https://openalex.org/W1990415687","https://openalex.org/W2001601711","https://openalex.org/W2018512374","https://openalex.org/W2019321194","https://openalex.org/W2027864161","https://openalex.org/W2029016187","https://openalex.org/W2037328180","https://openalex.org/W2037685751","https://openalex.org/W2042176005","https://openalex.org/W2045097502","https://openalex.org/W2052740339","https://openalex.org/W2064753173","https://openalex.org/W2068033618","https://openalex.org/W2073121395","https://openalex.org/W2083667801","https://openalex.org/W2087447148","https://openalex.org/W2091688845","https://openalex.org/W2094796465","https://openalex.org/W2101570837","https://openalex.org/W2112468172","https://openalex.org/W2121835925","https://openalex.org/W2150754026","https://openalex.org/W2164106566","https://openalex.org/W2167574130","https://openalex.org/W2168588397","https://openalex.org/W2949176902","https://openalex.org/W2962767870","https://openalex.org/W3098506897","https://openalex.org/W3104177617","https://openalex.org/W3125677211","https://openalex.org/W4230482580","https://openalex.org/W6615819268","https://openalex.org/W6641246249","https://openalex.org/W6823652426"],"related_works":["https://openalex.org/W2372962357","https://openalex.org/W2049597710","https://openalex.org/W2379970161","https://openalex.org/W2081621039","https://openalex.org/W2013821601","https://openalex.org/W4226204372","https://openalex.org/W3039998266","https://openalex.org/W3136772997","https://openalex.org/W1647716320","https://openalex.org/W2923883951"],"abstract_inverted_index":{"We":[0,27],"give":[1],"an":[2],"algorithmic":[3],"computation":[4],"for":[5],"the":[6,35,46,51,57,66,87],"height":[7],"of":[8,37,40,56,65],"Kauffman's":[9],"clock":[10],"lattice":[11,31],"obtained":[12,44],"from":[13,45],"a":[14,41],"knot":[15,47,58],"diagram":[16,48],"with":[17],"two":[18,52],"adjacent":[19],"regions":[20],"starred":[21],"and":[22,91],"without":[23],"crossing":[24],"information":[25],"specified.":[26],"show":[28],"that":[29],"this":[30],"is":[32,86],"more":[33],"familiarly":[34],"graph":[36,43,68,85],"perfect":[38],"matchings":[39],"bipartite":[42,67,84],"by":[49],"overlaying":[50],"dual":[53],"Tait":[54],"graphs":[55],"diagram.":[59],"Furthermore":[60],"we":[61],"prove":[62],"structural":[63],"properties":[64],"in":[69],"general.":[70],"This":[71],"setting":[72],"also":[73],"makes":[74],"evident":[75],"applications":[76],"to":[77,92],"Chebyshev":[78],"or":[79],"harmonic":[80],"knots,":[81],"whose":[82],"related":[83],"popular":[88],"grid":[89],"graph,":[90],"discrete":[93],"Morse":[94],"functions.":[95]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-14T06:11:07.267592","created_date":"2025-10-10T00:00:00"}
