{"id":"https://openalex.org/W1484927633","doi":"https://doi.org/10.37236/1646","title":"On the Dimer Problem and the Ising Problem in Finite 3-dimensional Lattices","display_name":"On the Dimer Problem and the Ising Problem in Finite 3-dimensional Lattices","publication_year":2002,"publication_date":"2002-07-08","ids":{"openalex":"https://openalex.org/W1484927633","doi":"https://doi.org/10.37236/1646","mag":"1484927633"},"language":"en","primary_location":{"id":"doi:10.37236/1646","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1646","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i1r30/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":false,"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":null,"license_id":null,"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":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i1r30/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038875605","display_name":"Martin Loebl","orcid":"https://orcid.org/0000-0001-7968-0376"},"institutions":[{"id":"https://openalex.org/I21250087","display_name":"Charles University","ror":"https://ror.org/024d6js02","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21250087"]}],"countries":["CZ"],"is_corresponding":true,"raw_author_name":"Martin Loebl","raw_affiliation_strings":["Department of Applied Mathematics and","Institute for Theoretical Computer Science (ITI) Charles University Malostranske n. 25, 118 00 Praha 1, Czech Republic"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and","institution_ids":[]},{"raw_affiliation_string":"Institute for Theoretical Computer Science (ITI) Charles University Malostranske n. 25, 118 00 Praha 1, Czech Republic","institution_ids":["https://openalex.org/I21250087"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5038875605"],"corresponding_institution_ids":["https://openalex.org/I21250087"],"apc_list":null,"apc_paid":null,"fwci":0.5793,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.54945652,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"9","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.998199999332428,"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"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.998199999332428,"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"}},{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9911999702453613,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9882000088691711,"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/pfaffian","display_name":"Pfaffian","score":0.9807273149490356},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7944323420524597},{"id":"https://openalex.org/keywords/ising-model","display_name":"Ising model","score":0.7694383859634399},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6323916912078857},{"id":"https://openalex.org/keywords/partition-function","display_name":"Partition function (quantum field theory)","score":0.6299269199371338},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.6009202003479004},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5570300817489624},{"id":"https://openalex.org/keywords/square-lattice-ising-model","display_name":"Square-lattice Ising model","score":0.41132909059524536},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.2515135705471039},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12531721591949463},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.11637577414512634}],"concepts":[{"id":"https://openalex.org/C2775956649","wikidata":"https://www.wikidata.org/wiki/Q1189744","display_name":"Pfaffian","level":2,"score":0.9807273149490356},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7944323420524597},{"id":"https://openalex.org/C51329190","wikidata":"https://www.wikidata.org/wiki/Q1076349","display_name":"Ising model","level":2,"score":0.7694383859634399},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6323916912078857},{"id":"https://openalex.org/C2778401447","wikidata":"https://www.wikidata.org/wiki/Q7140637","display_name":"Partition function (quantum field theory)","level":2,"score":0.6299269199371338},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.6009202003479004},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5570300817489624},{"id":"https://openalex.org/C49005734","wikidata":"https://www.wikidata.org/wiki/Q7581981","display_name":"Square-lattice Ising model","level":3,"score":0.41132909059524536},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.2515135705471039},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12531721591949463},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.11637577414512634},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.37236/1646","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1646","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i1r30/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":false,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.2.7725","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.2.7725","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_9/PostScriptfiles/v9i1r30.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.3.2134","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.2134","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_9/PDF/v9i1r30.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.68.2074","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.68.2074","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://kam.mff.cuni.cz/~kamserie/serie/clanky/2000/s507.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.71.2261","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.71.2261","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://kam.mff.cuni.cz/~kamserie/serie/clanky/2000/s506.ps","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1646","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1646","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i1r30/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":false,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320338206","display_name":"Fondo de Financiamiento de Centros de Investigaci\u00f3n en \u00c1reas Prioritarias","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1484927633.pdf","grobid_xml":"https://content.openalex.org/works/W1484927633.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W888038687","https://openalex.org/W1515970832","https://openalex.org/W1653035750","https://openalex.org/W1952454332","https://openalex.org/W1970824455","https://openalex.org/W1973523344","https://openalex.org/W2013200539","https://openalex.org/W2016832592","https://openalex.org/W2037389370","https://openalex.org/W2077319040","https://openalex.org/W2083567260","https://openalex.org/W2086333739","https://openalex.org/W2096486078","https://openalex.org/W2577053083","https://openalex.org/W3100747620","https://openalex.org/W3101326198","https://openalex.org/W4244121195","https://openalex.org/W4246402091"],"related_works":["https://openalex.org/W3209539671","https://openalex.org/W2024458749","https://openalex.org/W2944617580","https://openalex.org/W4288357902","https://openalex.org/W2382664089","https://openalex.org/W2000567571","https://openalex.org/W2787138325","https://openalex.org/W1985264093","https://openalex.org/W2047006621","https://openalex.org/W3124252402"],"abstract_inverted_index":{"We":[0,23],"present":[1],"a":[2],"new":[3],"expression":[4],"for":[5],"the":[6,10,14,19,25,45],"partition":[7,16,29],"function":[8,17],"of":[9,18,35,37,41],"dimer":[11],"arrangements":[12],"and":[13,39],"Ising":[15],"3-dimensional":[20],"cubic":[21,46],"lattice.":[22,47],"use":[24],"Pfaffian":[26],"method.":[27],"The":[28],"functions":[30],"are":[31],"expressed":[32],"by":[33],"means":[34],"expectations":[36],"determinants":[38],"Pfaffians":[40],"matrices":[42],"associated":[43],"with":[44]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}