{"id":"https://openalex.org/W1565851765","doi":"https://doi.org/10.37236/1226","title":"The Number of Solutions of $X^2=0$ in Triangular Matrices Over $GF(q)$","display_name":"The Number of Solutions of $X^2=0$ in Triangular Matrices Over $GF(q)$","publication_year":1995,"publication_date":"1995-12-01","ids":{"openalex":"https://openalex.org/W1565851765","doi":"https://doi.org/10.37236/1226","mag":"1565851765"},"language":"en","primary_location":{"id":"doi:10.37236/1226","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1226","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v3i1r2/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/v3i1r2/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015661806","display_name":"Shalosh B. Ekhad","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Shalosh B. Ekhad","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5058881306","display_name":"Doron Zeilberger","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Doron Zeilberger","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5015661806"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":24,"citation_normalized_percentile":{"value":0.0611484,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"3","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9975000023841858,"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/T11476","display_name":"Graph theory and applications","score":0.9975000023841858,"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":0.9940000176429749,"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"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.991599977016449,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9188825488090515},{"id":"https://openalex.org/keywords/triangular-matrix","display_name":"Triangular matrix","score":0.749951958656311},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7469894289970398},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.6994034051895142},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.6453225016593933},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5173170566558838},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3348574638366699},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.26301300525665283},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11833781003952026},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.06362614035606384}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9188825488090515},{"id":"https://openalex.org/C104528550","wikidata":"https://www.wikidata.org/wiki/Q506265","display_name":"Triangular matrix","level":3,"score":0.749951958656311},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7469894289970398},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.6994034051895142},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.6453225016593933},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5173170566558838},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3348574638366699},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26301300525665283},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11833781003952026},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.06362614035606384},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/1226","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1226","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v3i1r2/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"}],"best_oa_location":{"id":"doi:10.37236/1226","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1226","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v3i1r2/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":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1565851765.pdf","grobid_xml":"https://content.openalex.org/works/W1565851765.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W24120466","https://openalex.org/W1989264262","https://openalex.org/W6608025442"],"related_works":["https://openalex.org/W2007591537","https://openalex.org/W2478770834","https://openalex.org/W4299935675","https://openalex.org/W2952441146","https://openalex.org/W2022711451","https://openalex.org/W2403268247","https://openalex.org/W2795713253","https://openalex.org/W1561529953","https://openalex.org/W2084941670","https://openalex.org/W2039986365"],"abstract_inverted_index":{"We":[0],"prove":[1],"an":[2],"explicit":[3],"formula":[4,24],"for":[5],"the":[6,20],"number":[7],"of":[8],"$n":[9],"\\times":[10],"n$":[11],"upper":[12],"triangular":[13],"matrices,":[14],"over":[15],"$GF(q)$,":[16],"whose":[17],"square":[18],"is":[19],"zero":[21],"matrix.":[22],"This":[23],"was":[25],"recently":[26],"conjectured":[27],"by":[28],"Sasha":[29],"Kirillov":[30],"and":[31],"Anna":[32],"Melnikov.":[33]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"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"}