{"id":"https://openalex.org/W2149131753","doi":"https://doi.org/10.37236/3810","title":"Counting Symmetric Nilpotent Matrices","display_name":"Counting Symmetric Nilpotent Matrices","publication_year":2014,"publication_date":"2014-04-01","ids":{"openalex":"https://openalex.org/W2149131753","doi":"https://doi.org/10.37236/3810","mag":"2149131753"},"language":"en","primary_location":{"id":"doi:10.37236/3810","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3810","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v21i2p4/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/v21i2p4/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5105369849","display_name":"Andries E. Brouwer","orcid":null},"institutions":[{"id":"https://openalex.org/I100930933","display_name":"University College Dublin","ror":"https://ror.org/05m7pjf47","country_code":"IE","type":"education","lineage":["https://openalex.org/I100930933"]},{"id":"https://openalex.org/I32597200","display_name":"Ghent University","ror":"https://ror.org/00cv9y106","country_code":"BE","type":"education","lineage":["https://openalex.org/I32597200"]},{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["BE","IE","NL"],"is_corresponding":false,"raw_author_name":"Andries E. Brouwer","raw_affiliation_strings":["Department of Mathematics Technische Universiteit Eindhoven Netherlands","Department of Mathematics Universiteit Gent Belgium","School of Mathematical Sciences University College Dublin Ireland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Technische Universiteit Eindhoven Netherlands","institution_ids":["https://openalex.org/I83019370"]},{"raw_affiliation_string":"Department of Mathematics Universiteit Gent Belgium","institution_ids":["https://openalex.org/I32597200"]},{"raw_affiliation_string":"School of Mathematical Sciences University College Dublin Ireland","institution_ids":["https://openalex.org/I100930933"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111555804","display_name":"Rod Gow","orcid":null},"institutions":[{"id":"https://openalex.org/I100930933","display_name":"University College Dublin","ror":"https://ror.org/05m7pjf47","country_code":"IE","type":"education","lineage":["https://openalex.org/I100930933"]}],"countries":["IE"],"is_corresponding":false,"raw_author_name":"Rod Gow","raw_affiliation_strings":["University College Dublin"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University College Dublin","institution_ids":["https://openalex.org/I100930933"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038859418","display_name":"John Sheekey","orcid":"https://orcid.org/0000-0002-8590-0301"},"institutions":[{"id":"https://openalex.org/I32597200","display_name":"Ghent University","ror":"https://ror.org/00cv9y106","country_code":"BE","type":"education","lineage":["https://openalex.org/I32597200"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"John Sheekey","raw_affiliation_strings":["Universiteit Gent"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universiteit Gent","institution_ids":["https://openalex.org/I32597200"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5441,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.6472593,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"21","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.996399998664856,"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/T10849","display_name":"Finite Group Theory Research","score":0.996399998664856,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9957000017166138,"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"}},{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.9936000108718872,"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":0.9137901067733765},{"id":"https://openalex.org/keywords/nilpotent","display_name":"Nilpotent","score":0.7972782850265503},{"id":"https://openalex.org/keywords/bilinear-form","display_name":"Bilinear form","score":0.6240015625953674},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6080900430679321},{"id":"https://openalex.org/keywords/symmetric-bilinear-form","display_name":"Symmetric bilinear form","score":0.5875911712646484},{"id":"https://openalex.org/keywords/nilpotent-group","display_name":"Nilpotent group","score":0.5776268243789673},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5530234575271606},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.45485925674438477},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4285958409309387},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32174837589263916}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9137901067733765},{"id":"https://openalex.org/C50555996","wikidata":"https://www.wikidata.org/wiki/Q840023","display_name":"Nilpotent","level":2,"score":0.7972782850265503},{"id":"https://openalex.org/C8828549","wikidata":"https://www.wikidata.org/wiki/Q837924","display_name":"Bilinear form","level":2,"score":0.6240015625953674},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6080900430679321},{"id":"https://openalex.org/C79940087","wikidata":"https://www.wikidata.org/wiki/Q2100018","display_name":"Symmetric bilinear form","level":3,"score":0.5875911712646484},{"id":"https://openalex.org/C206219070","wikidata":"https://www.wikidata.org/wiki/Q1755242","display_name":"Nilpotent group","level":3,"score":0.5776268243789673},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5530234575271606},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.45485925674438477},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4285958409309387},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32174837589263916},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.37236/3810","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3810","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v21i2p4/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"},{"id":"pmh:oai:pure.tue.nl:openaire_cris_publications/8db66147-49ca-494e-8cdd-e47fc273b646","is_oa":true,"landing_page_url":"https://research.tue.nl/en/publications/8db66147-49ca-494e-8cdd-e47fc273b646","pdf_url":"https://pure.tue.nl/ws/files/3970738/696558105408389.pdf","source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Brouwer, A E, Gow, R & Sheekey, J 2014, 'Counting symmetric nilpotent matrices', The Electronic Journal of Combinatorics, vol. 21, no. 2, P2.4, pp. P2.4-1/16.","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:tue:oai:pure.tue.nl:publications/8db66147-49ca-494e-8cdd-e47fc273b646","is_oa":true,"landing_page_url":"https://research.tue.nl/nl/publications/8db66147-49ca-494e-8cdd-e47fc273b646","pdf_url":"https://research.tue.nl/nl/publications/8db66147-49ca-494e-8cdd-e47fc273b646","source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"The Electronic Journal of Combinatorics, 21(2):P2.4, P2.4 - 1/16. Electronic Journal of Combinatorics","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:773159","is_oa":false,"landing_page_url":"http://library.tue.nl/csp/dare/LinkToRepository.csp?recordnumber=773159","pdf_url":null,"source":{"id":"https://openalex.org/S4406923046","display_name":"TU/e Research Portal (Eindhoven University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN:1077-8926","raw_type":"Article / Letter to the editor"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.421.1666","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.421.1666","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.win.tue.nl/~aeb/preprints/countsymnilp.pdf","raw_type":"text"},{"id":"pmh:oai:library.tue.nl:773159","is_oa":false,"landing_page_url":"http://repository.tue.nl/773159","pdf_url":null,"source":{"id":"https://openalex.org/S4406923046","display_name":"TU/e Research Portal (Eindhoven University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN:1077-8926","raw_type":"Article / Letter to the editor"}],"best_oa_location":{"id":"doi:10.37236/3810","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3810","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v21i2p4/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":[{"score":0.46000000834465027,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321730","display_name":"Fonds Wetenschappelijk Onderzoek","ror":"https://ror.org/03qtxy027"},{"id":"https://openalex.org/F4320327336","display_name":"Vlaamse regering","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2149131753.pdf","grobid_xml":"https://content.openalex.org/works/W2149131753.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1577120613","https://openalex.org/W1603738076","https://openalex.org/W1974671107","https://openalex.org/W1977338085","https://openalex.org/W2049926609","https://openalex.org/W2068842980","https://openalex.org/W2090111100","https://openalex.org/W2138033161","https://openalex.org/W4298236575","https://openalex.org/W6603921870","https://openalex.org/W6829380851"],"related_works":["https://openalex.org/W2153554103","https://openalex.org/W2022486451","https://openalex.org/W3184171495","https://openalex.org/W2167486083","https://openalex.org/W1963546854","https://openalex.org/W2031905258","https://openalex.org/W1976845455","https://openalex.org/W4306710942","https://openalex.org/W4317211083","https://openalex.org/W1968215728"],"abstract_inverted_index":{"We":[0],"determine":[1],"the":[2,26],"number":[3,27],"of":[4,7,28],"nilpotent":[5,30],"matrices":[6],"order":[8],"$n$":[9],"over":[10],"$\\mathbb{F}_q$":[11],"that":[12],"are":[13],"self-adjoint":[14],"for":[15],"a":[16],"given":[17],"nondegenerate":[18],"symmetric":[19,29],"bilinear":[20],"form,":[21],"and":[22],"in":[23],"particular":[24],"find":[25],"matrices.":[31]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}