{"id":"https://openalex.org/W7220925704","doi":"https://doi.org/10.48550/arxiv.2610.10041","title":"A mathematical perspective on nonplanar on-shell forms","display_name":"A mathematical perspective on nonplanar on-shell forms","publication_year":2026,"publication_date":"2026-10-07","ids":{"openalex":"https://openalex.org/W7220925704","doi":"https://doi.org/10.48550/arxiv.2610.10041"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.10041","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10041","pdf_url":"https://arxiv.org/pdf/2610.10041","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/2610.10041","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5099173803","display_name":"Artyom Lisitsyn","orcid":"https://orcid.org/0009-0004-9071-0133","observed_orcids":["https://orcid.org/0009-0004-9071-0133"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lisitsyn, Artyom","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012749213","display_name":"Elizabeth Pratt","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pratt, Elizabeth","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091436729","display_name":"Melissa Sherman-Bennett","orcid":"https://orcid.org/0000-0003-3351-8837","observed_orcids":["https://orcid.org/0000-0003-3351-8837"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sherman-Bennett, Melissa","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5090966772","display_name":"Jaroslav Trnka","orcid":"https://orcid.org/0000-0003-2195-8093","observed_orcids":["https://orcid.org/0000-0003-2195-8093","https://orcid.org/0000-0003-4858-7528"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Trnka, Jaroslav","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9185000061988831,"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":0.9185000061988831,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.03909999877214432,"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/T10025","display_name":"Black Holes and Theoretical Physics","score":0.010999999940395355,"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/grassmannians","display_name":"Grassmannians","score":0.7549999952316284},{"id":"https://openalex.org/keywords/determinantal-formula","display_name":"determinantal formula","score":0.7910000085830688},{"id":"https://openalex.org/keywords/totally-nonnegative-grassmannian","display_name":"totally nonnegative Grassmannian","score":0.9599999785423279},{"id":"https://openalex.org/keywords/moduli-space-of-curves","display_name":"moduli space of curves","score":0.6970000267028809},{"id":"https://openalex.org/keywords/tropical-geometry","display_name":"tropical geometry","score":0.5149999856948853},{"id":"https://openalex.org/keywords/scattering-amplitudes","display_name":"scattering amplitudes","score":0.7559999823570251}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7724000215530396},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6090999841690063},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.5982999801635742},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.5525000095367432},{"id":"https://openalex.org/C97654310","wikidata":"https://www.wikidata.org/wiki/Q574023","display_name":"Hyperbolic tree","level":4,"score":0.453000009059906},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.44769999384880066},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.43459999561309814},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.40130001306533813},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.3652999997138977},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36410000920295715},{"id":"https://openalex.org/C162929932","wikidata":"https://www.wikidata.org/wiki/Q129638","display_name":"Grassmannian","level":2,"score":0.35989999771118164},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.35510000586509705},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.35269999504089355},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.3375000059604645},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3041999936103821},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2928999960422516},{"id":"https://openalex.org/C130327152","wikidata":"https://www.wikidata.org/wiki/Q748349","display_name":"Mathematical structure","level":2,"score":0.2913999855518341},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.27219998836517334},{"id":"https://openalex.org/C2779193601","wikidata":"https://www.wikidata.org/wiki/Q20026918","display_name":"Mathematical theory","level":2,"score":0.2637999951839447},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.2563999891281128},{"id":"https://openalex.org/C115071613","wikidata":"https://www.wikidata.org/wiki/Q1047080","display_name":"Differential form","level":2,"score":0.25540000200271606},{"id":"https://openalex.org/C64339825","wikidata":"https://www.wikidata.org/wiki/Q722659","display_name":"Graph property","level":5,"score":0.2547000050544739}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.10041","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10041","pdf_url":"https://arxiv.org/pdf/2610.10041","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.2610.10041","doi":"https://doi.org/10.48550/arxiv.2610.10041","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.10041","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.10041","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10041","pdf_url":"https://arxiv.org/pdf/2610.10041","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/W7220925704.pdf","grobid_xml":"https://content.openalex.org/works/W7220925704.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W1593193619","https://openalex.org/W1672638072","https://openalex.org/W4304731961","https://openalex.org/W4401355902","https://openalex.org/W7118010908"],"related_works":["https://openalex.org/W6940495378","https://openalex.org/W3104544624","https://openalex.org/W7118010908","https://openalex.org/W2509602848","https://openalex.org/W2497364444","https://openalex.org/W7097882468","https://openalex.org/W4311682471","https://openalex.org/W2494599472","https://openalex.org/W2500488687","https://openalex.org/W1598129858"],"abstract_inverted_index":{"On-shell":[0],"forms":[1,4,28,65,95,110],"are":[2,14],"differential":[3],"on":[5,32],"the":[6,33,36,52,55,78,104,112],"Grassmannian":[7],"which":[8,41,96],"arise":[9],"in":[10,40,51,99],"particle":[11],"physics.":[12],"They":[13],"defined":[15],"using":[16],"bipartite":[17],"graphs":[18],"with":[19],"$n$":[20],"distinguished":[21],"``boundary''":[22],"vertices.":[23],"Mathematical":[24],"investigation":[25],"of":[26,54,93,109,115],"on-shell":[27,64,94],"has":[29],"largely":[30],"focused":[31],"case":[34,42,80],"where":[35],"graph":[37],"is":[38],"planar,":[39],"one":[43],"can":[44],"utilize":[45],"combinatorial":[46],"tools":[47,76],"pioneered":[48],"by":[49,118],"Postnikov":[50],"study":[53],"totally":[56],"nonnegative":[57],"Grassmannian.":[58],"In":[59],"this":[60,107],"article,":[61],"we":[62],"investigate":[63],"for":[66,90],"arbitrary":[67,82],"graphs.":[68,83],"We":[69,84,102],"first":[70,97],"discuss":[71],"how":[72],"to":[73,81],"extend":[74],"various":[75],"from":[77],"planar":[79],"then":[85],"prove":[86],"a":[87,91],"determinantal":[88],"formula":[89],"class":[92,108],"appeared":[98],"physics":[100],"literature.":[101],"explain":[103],"relation":[105],"between":[106],"and":[111],"hypertree":[113],"divisors":[114],"$M_{0,n}$,":[116],"introduced":[117],"Castravet--Tevelev.":[119]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-09T00:00:00"}
