{"id":"https://openalex.org/W3135732801","doi":"https://doi.org/10.37236/10294","title":"Automorphisms and Some Geodesic Properties of Ortho-Grassmann Graphs","display_name":"Automorphisms and Some Geodesic Properties of Ortho-Grassmann Graphs","publication_year":2021,"publication_date":"2021-12-17","ids":{"openalex":"https://openalex.org/W3135732801","doi":"https://doi.org/10.37236/10294","mag":"3135732801"},"language":"en","primary_location":{"id":"doi:10.37236/10294","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10294","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i4p49/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/v28i4p49/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060769535","display_name":"Mark Pankov","orcid":"https://orcid.org/0000-0003-2052-0348"},"institutions":[{"id":"https://openalex.org/I47996466","display_name":"University of Warmia and Mazury in Olsztyn","ror":"https://ror.org/05s4feg49","country_code":"PL","type":"education","lineage":["https://openalex.org/I47996466"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Mark Pankov","raw_affiliation_strings":["Faculty of Mathematics and Computer Science University of Warmia and Mazury S loneczna 54, 10-710 Olsztyn, Poland"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science University of Warmia and Mazury S loneczna 54, 10-710 Olsztyn, Poland","institution_ids":["https://openalex.org/I47996466"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002009647","display_name":"Krzysztof Petelczyc","orcid":"https://orcid.org/0000-0003-0500-9699"},"institutions":[{"id":"https://openalex.org/I245364917","display_name":"University of Bia\u0142ystok","ror":"https://ror.org/01qaqcf60","country_code":"PL","type":"education","lineage":["https://openalex.org/I245364917"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Krzysztof Petelczyc","raw_affiliation_strings":["Faculty of Mathematics University of Bia lystok Cio lkowskiego 1M, 15-245 Bia lystok, Poland"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics University of Bia lystok Cio lkowskiego 1M, 15-245 Bia lystok, Poland","institution_ids":["https://openalex.org/I245364917"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022425329","display_name":"Mariusz \u017bynel","orcid":"https://orcid.org/0000-0001-9297-4774"},"institutions":[{"id":"https://openalex.org/I245364917","display_name":"University of Bia\u0142ystok","ror":"https://ror.org/01qaqcf60","country_code":"PL","type":"education","lineage":["https://openalex.org/I245364917"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Mariusz \u0179ynel","raw_affiliation_strings":["Faculty of Mathematics University of Bia lystok Cio lkowskiego 1M, 15-245 Bia lystok, Poland"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics University of Bia lystok Cio lkowskiego 1M, 15-245 Bia lystok, Poland","institution_ids":["https://openalex.org/I245364917"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5060769535"],"corresponding_institution_ids":["https://openalex.org/I47996466"],"apc_list":null,"apc_paid":null,"fwci":0.9852,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.70203803,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"28","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.9961000084877014,"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":0.8942227959632874},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.71089768409729},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6833528280258179},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.577949047088623},{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.45518678426742554},{"id":"https://openalex.org/keywords/unitary-state","display_name":"Unitary state","score":0.44382309913635254},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.425055593252182},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.342506468296051},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32783597707748413},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07509663701057434}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8942227959632874},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.71089768409729},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6833528280258179},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.577949047088623},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.45518678426742554},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.44382309913635254},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.425055593252182},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.342506468296051},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32783597707748413},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07509663701057434},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/10294","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10294","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i4p49/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:10.37236/10294","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10294","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i4p49/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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3135732801.pdf","grobid_xml":"https://content.openalex.org/works/W3135732801.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W178185666","https://openalex.org/W595049502","https://openalex.org/W1647987060","https://openalex.org/W1970124693","https://openalex.org/W2153142809","https://openalex.org/W2313238767","https://openalex.org/W2316105632","https://openalex.org/W2963394320","https://openalex.org/W3000300545","https://openalex.org/W3100704234","https://openalex.org/W3171249079","https://openalex.org/W4210668185","https://openalex.org/W4238005091"],"related_works":["https://openalex.org/W2391321755","https://openalex.org/W2114124567","https://openalex.org/W2896134808","https://openalex.org/W2998724919","https://openalex.org/W4211228991","https://openalex.org/W2949110394","https://openalex.org/W161787318","https://openalex.org/W2353790329","https://openalex.org/W2279743781","https://openalex.org/W3019634500"],"abstract_inverted_index":{"Let":[0],"$H$":[1,18],"be":[2],"a":[3,72,89],"complex":[4],"Hilbert":[5],"space.":[6],"Consider":[7],"the":[8,58,97,104,108,113,143],"ortho-Grassmann":[9,127,140,151],"graph":[10,33],"$\\Gamma^{\\perp}_{k}(H)$":[11,68,85],"whose":[12],"vertices":[13],"are":[14,26,36],"$k$-dimensional":[15],"subspaces":[16,25],"of":[17,20,51,67,84,99,123,135,157],"(projections":[19],"rank":[21,52],"$k$)":[22],"and":[23,38,45,103,129,139],"two":[24,125],"connected":[27],"by":[28,71,88],"an":[29,49,101],"edge":[30],"in":[31,126,133,137],"this":[32,118,147],"if":[34,60,77],"they":[35],"compatible":[37],"adjacent":[39],"(the":[40],"corresponding":[41],"rank-$k$":[42],"projections":[43],"commute":[44],"their":[46],"difference":[47],"is":[48,57,69,86,96],"operator":[50,93],"$2$).":[53],"Our":[54],"main":[55],"result":[56,148],"following:":[59],"$\\dim":[61,78,111],"H\\ne":[62],"2k$,":[63],"then":[64,81],"every":[65,82],"automorphism":[66,83,102],"induced":[70,87],"unitary":[73,90],"or":[74,91,94],"anti-unitary":[75,92],"operator;":[76],"H=2k\\ge":[79],"6$,":[80],"it":[95],"composition":[98],"such":[100],"orthocomplementary":[105],"map.":[106],"For":[107],"case":[109],"when":[110],"H=2k=4$":[112],"statement":[114,119],"fails.":[115],"To":[116],"prove":[117],"we":[120,145],"compare":[121],"geodesics":[122,136],"length":[124],"graphs":[128,152],"characterise":[130],"compatibility":[131],"(commutativity)":[132],"terms":[134],"Grassmann":[138],"graphs.":[141],"At":[142],"end,":[144],"extend":[146],"on":[149],"generalised":[150],"associated":[153],"to":[154],"conjugacy":[155],"classes":[156],"finite-rank":[158],"self-adjoint":[159],"operators.":[160]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
