{"id":"https://openalex.org/W7214925892","doi":"https://doi.org/10.48550/arxiv.2609.38030","title":"Diagrammatic construction of GKZ systems for polygonal functions","display_name":"Diagrammatic construction of GKZ systems for polygonal functions","publication_year":2026,"publication_date":"2026-09-29","ids":{"openalex":"https://openalex.org/W7214925892","doi":"https://doi.org/10.48550/arxiv.2609.38030"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.38030","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.38030","pdf_url":"https://arxiv.org/pdf/2609.38030","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.38030","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5153681840","display_name":"K. B. Alkalaev","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I19880235","display_name":"Lomonosov Moscow State University","ror":"https://ror.org/010pmpe69","country_code":"RU","type":"education","lineage":["https://openalex.org/I19880235"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Alkalaev, K. B.","raw_affiliation_strings":["Institute for Theoretical and Mathematical Physics , Lomonosov Moscow State University , 119991 Moscow , Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Theoretical and Mathematical Physics , Lomonosov Moscow State University , 119991 Moscow , Russia","institution_ids":["https://openalex.org/I19880235"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074385347","display_name":"Semyon Mandrygin","orcid":"https://orcid.org/0000-0001-5126-6392","observed_orcids":["https://orcid.org/0000-0001-5126-6392"]},"institutions":[{"id":"https://openalex.org/I118517470","display_name":"P.N. Lebedev Physical Institute of the Russian Academy of Sciences","ror":"https://ror.org/01jkd3546","country_code":"RU","type":"facility","lineage":["https://openalex.org/I118517470","https://openalex.org/I1313323035","https://openalex.org/I2800498218","https://openalex.org/I4210096333"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Mandrygin, Semyon","raw_affiliation_strings":["Department of Theoretical Physics , P.N. Lebedev Physical Institute , 119991 Moscow , Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Theoretical Physics , P.N. Lebedev Physical Institute , 119991 Moscow , Russia","institution_ids":["https://openalex.org/I118517470"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5153600486","display_name":"Y. M. Zalishchansky","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I118517470","display_name":"P.N. Lebedev Physical Institute of the Russian Academy of Sciences","ror":"https://ror.org/01jkd3546","country_code":"RU","type":"facility","lineage":["https://openalex.org/I118517470","https://openalex.org/I1313323035","https://openalex.org/I2800498218","https://openalex.org/I4210096333"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Zalishchansky, Y. M.","raw_affiliation_strings":["Department of Theoretical Physics , P.N. Lebedev Physical Institute , 119991 Moscow , Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Theoretical Physics , P.N. Lebedev Physical Institute , 119991 Moscow , Russia","institution_ids":["https://openalex.org/I118517470"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.35109999775886536,"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"}},"topics":[{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.35109999775886536,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.1509000062942505,"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/T10025","display_name":"Black Holes and Theoretical Physics","score":0.1460999995470047,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/appell-functions","display_name":"Appell functions","score":0.8930000066757202},{"id":"https://openalex.org/keywords/planar-diagrams","display_name":"planar diagrams","score":0.5249999761581421}],"concepts":[{"id":"https://openalex.org/C106624574","wikidata":"https://www.wikidata.org/wiki/Q5270387","display_name":"Diagrammatic reasoning","level":2,"score":0.9473999738693237},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6323000192642212},{"id":"https://openalex.org/C197320386","wikidata":"https://www.wikidata.org/wiki/Q21028472","display_name":"Hypergeometric function","level":2,"score":0.5189999938011169},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5181999802589417},{"id":"https://openalex.org/C176671685","wikidata":"https://www.wikidata.org/wiki/Q730600","display_name":"Hypergeometric distribution","level":2,"score":0.5048999786376953},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.49869999289512634},{"id":"https://openalex.org/C98214594","wikidata":"https://www.wikidata.org/wiki/Q850275","display_name":"Conformal map","level":2,"score":0.48899999260902405},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.48669999837875366},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.47929999232292175},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.4641999900341034},{"id":"https://openalex.org/C99636146","wikidata":"https://www.wikidata.org/wiki/Q35889","display_name":"Parametric equation","level":2,"score":0.43290001153945923},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.41200000047683716},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3831999897956848},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.3310999870300293},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.32499998807907104},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.3228999972343445},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.3059999942779541},{"id":"https://openalex.org/C181881257","wikidata":"https://www.wikidata.org/wiki/Q4780998","display_name":"Appell series","level":5,"score":0.25380000472068787}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.38030","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.38030","pdf_url":"https://arxiv.org/pdf/2609.38030","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.38030","doi":"https://doi.org/10.48550/arxiv.2609.38030","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.38030","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.38030","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.38030","pdf_url":"https://arxiv.org/pdf/2609.38030","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214925892.pdf","grobid_xml":"https://content.openalex.org/works/W7214925892.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W1970198451","https://openalex.org/W1985777033","https://openalex.org/W2015530957","https://openalex.org/W2027238935","https://openalex.org/W4293150342"],"related_works":["https://openalex.org/W4213235656","https://openalex.org/W2970586712","https://openalex.org/W3099576129","https://openalex.org/W2133806896","https://openalex.org/W2035379809","https://openalex.org/W3045744769","https://openalex.org/W6907262233","https://openalex.org/W4399551841","https://openalex.org/W4361863956","https://openalex.org/W2083203628"],"abstract_inverted_index":{"We":[0,114],"investigate":[1],"the":[2,49,62,68,73,82,106,116,127,131],"recently":[3],"introduced":[4],"polygonal":[5,44,124],"hypergeometric":[6,52],"functions":[7,24],"[arXiv:2502.12127,":[8],"arXiv:2507.01904],":[9],"which":[10,54,65],"are":[11],"conjectured":[12],"to":[13],"evaluate":[14],"multipoint":[15],"parametric":[16],"one-loop":[17],"conformal":[18],"integrals":[19],"in":[20,35],"arbitrary":[21],"dimensions.":[22],"These":[23],"can":[25],"be":[26],"systematically":[27],"constructed":[28],"using":[29],"a":[30,79,89],"diagrammatic":[31,58,70],"algorithm":[32],"that":[33],"operates":[34],"terms":[36],"of":[37,81,84,92,100,123],"simple":[38],"planar":[39],"shapes.":[40],"Given":[41],"an":[42,56],"$n$-point":[43],"power":[45],"series,":[46],"we":[47],"formulate":[48],"corresponding":[50,74],"GKZ":[51],"system,":[53],"admits":[55],"explicit":[57],"interpretation.":[59],"In":[60],"particular,":[61],"transianic":[63],"matrix,":[64],"encodes":[66],"all":[67],"relevant":[69],"data,":[71],"determines":[72],"toric":[75,94,108],"matrix":[76],"along":[77],"with":[78,119],"basis":[80],"lattice":[83],"relations,":[85],"thereby":[86],"singling":[87],"out":[88],"finite":[90,97],"subsystem":[91,98],"$n(n-3)/2$":[93],"equations.":[95],"This":[96],"consists":[99],"second-":[101],"and":[102,130],"third-order":[103],"equations,":[104],"whereas":[105],"full":[107],"family":[109],"also":[110],"includes":[111],"higher-order":[112],"ones.":[113],"illustrate":[115],"general":[117],"procedure":[118],"several":[120],"prominent":[121],"examples":[122],"functions,":[125],"including":[126],"fourth":[128],"Appell":[129],"Srivastava--Daoust":[132],"functions.":[133]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-01T00:00:00"}