{"id":"https://openalex.org/W7214790729","doi":"https://doi.org/10.48550/arxiv.2609.33979","title":"Edge-Defect Spectral Methods for Higher-Order Rankings of Spanning Tree Counts","display_name":"Edge-Defect Spectral Methods for Higher-Order Rankings of Spanning Tree Counts","publication_year":2026,"publication_date":"2026-09-27","ids":{"openalex":"https://openalex.org/W7214790729","doi":"https://doi.org/10.48550/arxiv.2609.33979"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.33979","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.33979","pdf_url":"https://arxiv.org/pdf/2609.33979","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/2609.33979","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070419116","display_name":"Shunya Tamura","orcid":"https://orcid.org/0009-0000-2162-2536","observed_orcids":["https://orcid.org/0009-0000-2162-2536"]},"institutions":[{"id":"https://openalex.org/I2799799709","display_name":"Saitama Prefecture","ror":"https://ror.org/03ykm7q16","country_code":"JP","type":"other","lineage":["https://openalex.org/I2799799709"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Tamura, Shunya","raw_affiliation_strings":["City Okegawa West Junior High School 3680-1 Kawataya , Okegawa , Saitama 363-0027 , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"City Okegawa West Junior High School 3680-1 Kawataya , Okegawa , Saitama 363-0027 , Japan","institution_ids":["https://openalex.org/I2799799709"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108093060","display_name":"Jos\u00e9 Luis Palacios","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I169521973","display_name":"University of New Mexico","ror":"https://ror.org/05fs6jp91","country_code":"US","type":"education","lineage":["https://openalex.org/I169521973"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Palacios, Jos\u00e9 Luis","raw_affiliation_strings":["Department of Electrical and Computer Engineering , University of New Mexico Albuquerque , NM 87131 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering , University of New Mexico Albuquerque , NM 87131 , USA","institution_ids":["https://openalex.org/I169521973"]}]}],"institutions":[],"countries_distinct_count":2,"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/T11476","display_name":"Graph theory and applications","score":0.9609000086784363,"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/T11476","display_name":"Graph theory and applications","score":0.9609000086784363,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.01549999974668026,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.008899999782443047,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/edge-deletion","display_name":"edge deletion","score":0.5479999780654907},{"id":"https://openalex.org/keywords/complete-graphs","display_name":"complete graphs","score":0.7540000081062317},{"id":"https://openalex.org/keywords/stability-inequalities","display_name":"stability inequalities","score":0.8889999985694885},{"id":"https://openalex.org/keywords/isomorphism-classes","display_name":"isomorphism classes","score":0.6930000185966492},{"id":"https://openalex.org/keywords/logarithmic-expansion","display_name":"logarithmic expansion","score":0.7770000100135803},{"id":"https://openalex.org/keywords/graph-enumeration","display_name":"graph enumeration","score":0.5040000081062317}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8632000088691711},{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.7886000275611877},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6482999920845032},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5649999976158142},{"id":"https://openalex.org/C13743678","wikidata":"https://www.wikidata.org/wiki/Q240464","display_name":"Minimum spanning tree","level":2,"score":0.5439000129699707},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5164999961853027},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.43799999356269836},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.4025999903678894},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36250001192092896},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.35440000891685486},{"id":"https://openalex.org/C63645285","wikidata":"https://www.wikidata.org/wiki/Q797860","display_name":"Kruskal's algorithm","level":3,"score":0.3262999951839447},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3000999987125397},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.25060001015663147}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.33979","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.33979","pdf_url":"https://arxiv.org/pdf/2609.33979","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.2609.33979","doi":"https://doi.org/10.48550/arxiv.2609.33979","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.33979","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:2609.33979","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.33979","pdf_url":"https://arxiv.org/pdf/2609.33979","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214790729.pdf","grobid_xml":"https://content.openalex.org/works/W7214790729.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W7201852016","https://openalex.org/W7204483803"],"related_works":["https://openalex.org/W7204483803","https://openalex.org/W7204787209","https://openalex.org/W7201852016","https://openalex.org/W6937157494","https://openalex.org/W2080314023","https://openalex.org/W2058397373","https://openalex.org/W1888793072","https://openalex.org/W3126158518","https://openalex.org/W2051765964","https://openalex.org/W7097970499"],"abstract_inverted_index":{"In":[0],"this":[1,65],"paper,":[2],"we":[3,44,78],"study":[4],"the":[5,26,31,35,39,52,55,61,83,88,99,102,105,109,113,116,126],"higher-order":[6],"ranking,":[7],"by":[8,18,30],"spanning-tree":[9,90,128],"count,":[10],"of":[11,23,57,71,108,118,125],"graphs":[12,73,86],"obtained":[13],"from":[14,60],"a":[15,20,46,69,122],"complete":[16],"graph":[17],"deleting":[19],"fixed":[21],"number":[22,37,56,117],"edges.":[24],"Using":[25],"edge-defect":[27],"matrix":[28],"determined":[29],"deleted":[32],"edges":[33],"and":[34,94,112],"interaction":[36,76,103],"measuring":[38],"local":[40,106],"overlap":[41],"among":[42],"them,":[43],"derive":[45],"stability":[47,66],"inequality":[48],"that":[49],"quantitatively":[50],"estimates":[51],"decrease":[53,114],"in":[54,115],"spanning":[58,119],"trees":[59,120],"matching-deletion":[62],"case.":[63],"Combining":[64],"estimate":[67],"with":[68,87],"classification":[70],"deletion":[72,85,110],"having":[74],"small":[75],"number,":[77,104],"determine,":[79],"up":[80],"to":[81],"isomorphism,":[82],"nine":[84],"largest":[89],"counts":[91],"for":[92],"$p\\geq6$":[93],"$n\\geq2p$.":[95],"We":[96],"also":[97],"clarify":[98],"relation":[100],"between":[101],"structure":[107],"graph,":[111],"through":[121],"logarithmic":[123],"expansion":[124],"normalized":[127],"count.":[129]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-30T00:00:00"}