{"id":"https://openalex.org/W2992816870","doi":"https://doi.org/10.37236/1781","title":"Weighted Aztec Diamond Graphs and the Weyl Character Formula","display_name":"Weighted Aztec Diamond Graphs and the Weyl Character Formula","publication_year":2004,"publication_date":"2004-04-02","ids":{"openalex":"https://openalex.org/W2992816870","doi":"https://doi.org/10.37236/1781","mag":"2992816870"},"language":"en","primary_location":{"id":"doi:10.37236/1781","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1781","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v11i1r28/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":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":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v11i1r28/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061530239","display_name":"Georgia Benkart","orcid":null},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]},{"id":"https://openalex.org/I72509657","display_name":"Epic Systems (United States)","ror":"https://ror.org/029z3g861","country_code":"US","type":"company","lineage":["https://openalex.org/I72509657"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Georgia Benkart","raw_affiliation_strings":["Department of Mathematics University of Wisconsin Madison, WI 53706","Epic Systems Corporation 5301 Tokay Blvd. Madison, WI 53711"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics University of Wisconsin Madison, WI 53706","institution_ids":["https://openalex.org/I135310074"]},{"raw_affiliation_string":"Epic Systems Corporation 5301 Tokay Blvd. Madison, WI 53711","institution_ids":["https://openalex.org/I72509657"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083623863","display_name":"Oliver D. Eng","orcid":null},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]},{"id":"https://openalex.org/I72509657","display_name":"Epic Systems (United States)","ror":"https://ror.org/029z3g861","country_code":"US","type":"company","lineage":["https://openalex.org/I72509657"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Oliver Eng","raw_affiliation_strings":["Department of Mathematics University of Wisconsin Madison, WI 53706","Epic Systems Corporation 5301 Tokay Blvd. Madison, WI 53711"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics University of Wisconsin Madison, WI 53706","institution_ids":["https://openalex.org/I135310074"]},{"raw_affiliation_string":"Epic Systems Corporation 5301 Tokay Blvd. Madison, WI 53711","institution_ids":["https://openalex.org/I72509657"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5061530239"],"corresponding_institution_ids":["https://openalex.org/I135310074","https://openalex.org/I72509657"],"apc_list":null,"apc_paid":null,"fwci":1.0369,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.77411537,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"11","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":1.0,"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":1.0,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9997000098228455,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.9154760837554932},{"id":"https://openalex.org/keywords/monomial","display_name":"Monomial","score":0.8973391652107239},{"id":"https://openalex.org/keywords/character","display_name":"Character (mathematics)","score":0.6536100506782532},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6104296445846558},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4740048348903656},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.43872931599617004},{"id":"https://openalex.org/keywords/representation-theory","display_name":"Representation theory","score":0.4134898781776428},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3018604516983032},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0674884021282196}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9154760837554932},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.8973391652107239},{"id":"https://openalex.org/C2780861071","wikidata":"https://www.wikidata.org/wiki/Q1062934","display_name":"Character (mathematics)","level":2,"score":0.6536100506782532},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6104296445846558},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4740048348903656},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.43872931599617004},{"id":"https://openalex.org/C197273675","wikidata":"https://www.wikidata.org/wiki/Q13220368","display_name":"Representation theory","level":2,"score":0.4134898781776428},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3018604516983032},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0674884021282196}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/1781","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1781","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v11i1r28/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":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:10.1.1.10.575","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.10.575","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_11/PostScriptfiles/v11i1r28.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.5.6478","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.5.6478","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_11/PDF/v11i1r28.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1781","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1781","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v11i1r28/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":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":[{"id":"https://openalex.org/G8355201632","display_name":"Combinatorics and Representation Theory","funder_award_id":"9970119","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2992816870.pdf","grobid_xml":"https://content.openalex.org/works/W2992816870.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W1565930783","https://openalex.org/W1695430876","https://openalex.org/W1746987937","https://openalex.org/W1991885341","https://openalex.org/W2030077996","https://openalex.org/W2109934391","https://openalex.org/W2135205597","https://openalex.org/W2168654091","https://openalex.org/W2949089804","https://openalex.org/W2952206299","https://openalex.org/W4243402039","https://openalex.org/W4255251055","https://openalex.org/W6648330834","https://openalex.org/W6676708868","https://openalex.org/W6764296675"],"related_works":["https://openalex.org/W2399505800","https://openalex.org/W333749553","https://openalex.org/W1966623661","https://openalex.org/W2942288111","https://openalex.org/W2951675266","https://openalex.org/W2039516134","https://openalex.org/W1653027350","https://openalex.org/W2377423215","https://openalex.org/W2949676024","https://openalex.org/W4297903630"],"abstract_inverted_index":{"Special":[0],"weight":[1,18,48],"labelings":[2],"on":[3],"Aztec":[4],"diamond":[5],"graphs":[6],"lead":[7],"to":[8,20,38],"sum-product":[9],"identities":[10,33],"through":[11],"a":[12,28],"recursive":[13],"formula":[14,42],"of":[15,24,53],"Kuo.":[16],"The":[17],"assigned":[19],"each":[21],"perfect":[22],"matching":[23],"the":[25,32,44,54,58],"graph":[26],"is":[27],"Laurent":[29],"monomial,":[30],"and":[31],"in":[34],"these":[35],"monomials":[36],"combine":[37],"give":[39],"Weyl's":[40],"character":[41],"for":[43,57],"representation":[45],"with":[46],"highest":[47],"$\\rho$":[49],"(the":[50],"half":[51],"sum":[52],"positive":[55],"roots)":[56],"classical":[59],"Lie":[60],"algebras.":[61]},"counts_by_year":[{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}