{"id":"https://openalex.org/W7203673897","doi":"https://doi.org/10.48550/arxiv.2608.15398","title":"On the Laplacian spectral gap of generalized pancake graphs","display_name":"On the Laplacian spectral gap of generalized pancake graphs","publication_year":2026,"publication_date":"2026-08-15","ids":{"openalex":"https://openalex.org/W7203673897","doi":"https://doi.org/10.48550/arxiv.2608.15398"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.15398","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.15398","pdf_url":"https://arxiv.org/pdf/2608.15398","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-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","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/2608.15398","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101787512","display_name":"Sa\u00fal A. Blanco","orcid":"https://orcid.org/0000-0003-2315-5331","observed_orcids":["https://orcid.org/0000-0003-2315-5331"]},"institutions":[{"id":"https://openalex.org/I4210119109","display_name":"Indiana University Bloomington","ror":"https://ror.org/02k40bc56","country_code":"US","type":"education","lineage":["https://openalex.org/I4210119109","https://openalex.org/I592451"]},{"id":"https://openalex.org/I592451","display_name":"Indiana University","ror":"https://ror.org/01kg8sb98","country_code":"US","type":"education","lineage":["https://openalex.org/I592451"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Blanco, Sa\u00fal A.","raw_affiliation_strings":["Department of Computer Science . Indiana University , Bloomington "],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science . Indiana University , Bloomington ","institution_ids":["https://openalex.org/I4210119109","https://openalex.org/I592451"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101787512"],"corresponding_institution_ids":["https://openalex.org/I4210119109","https://openalex.org/I592451"],"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/T10849","display_name":"Finite Group Theory Research","score":0.7875999808311462,"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":0.7875999808311462,"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/T11476","display_name":"Graph theory and applications","score":0.1071000024676323,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.02889999933540821,"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/cayley-graphs","display_name":"Cayley graphs","score":0.8169999718666077},{"id":"https://openalex.org/keywords/spectral-gap","display_name":"spectral gap","score":0.7789999842643738},{"id":"https://openalex.org/keywords/normalized-laplacian-matrix","display_name":"normalized Laplacian","score":0.9879999756813049},{"id":"https://openalex.org/keywords/colored-permutations","display_name":"colored permutations","score":0.6520000100135803},{"id":"https://openalex.org/keywords/wreath-products","display_name":"wreath products","score":0.6510000228881836},{"id":"https://openalex.org/keywords/expander-graphs","display_name":"expander graphs","score":0.8429999947547913},{"id":"https://openalex.org/keywords/fourier-decomposition","display_name":"Fourier decomposition","score":0.5870000123977661}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8464999794960022},{"id":"https://openalex.org/C120204988","wikidata":"https://www.wikidata.org/wiki/Q859174","display_name":"Cayley graph","level":3,"score":0.7925999760627747},{"id":"https://openalex.org/C2778114796","wikidata":"https://www.wikidata.org/wiki/Q7575194","display_name":"Spectral gap","level":2,"score":0.6233000159263611},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5720000267028809},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5590000152587891},{"id":"https://openalex.org/C85307737","wikidata":"https://www.wikidata.org/wiki/Q751969","display_name":"Coset","level":2,"score":0.505299985408783},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.46140000224113464},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.45829999446868896},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.446399986743927},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.4447999894618988},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.35499998927116394},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.3427000045776367},{"id":"https://openalex.org/C154547637","wikidata":"https://www.wikidata.org/wiki/Q776602","display_name":"Expander graph","level":3,"score":0.31470000743865967},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.27000001072883606},{"id":"https://openalex.org/C198414033","wikidata":"https://www.wikidata.org/wiki/Q5155607","display_name":"Comparability graph","level":5,"score":0.2639000117778778},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.26010000705718994},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.26010000705718994},{"id":"https://openalex.org/C2985906921","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Spectral properties","level":2,"score":0.2565999925136566}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.15398","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.15398","pdf_url":"https://arxiv.org/pdf/2608.15398","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-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.15398","doi":"https://doi.org/10.48550/arxiv.2608.15398","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.15398","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:2608.15398","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.15398","pdf_url":"https://arxiv.org/pdf/2608.15398","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-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","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/W7203673897.pdf","grobid_xml":"https://content.openalex.org/works/W7203673897.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7135093712","https://openalex.org/W2742446643","https://openalex.org/W2736497107","https://openalex.org/W4226458306","https://openalex.org/W4385596916","https://openalex.org/W4383264401","https://openalex.org/W2983689388","https://openalex.org/W4389649535","https://openalex.org/W2021172574","https://openalex.org/W2886702391"],"abstract_inverted_index":{"The":[0,65],"generalized":[1,20,117],"pancake":[2,118],"graph":[3,8,85,147],"$P(m,n)$":[4],"is":[5,44,61,97],"the":[6,10,32,37,77,114,140,144,149],"Cayley":[7,146],"of":[9,12,36,76,86,105,133,143],"group":[11],"colored":[13],"permutations":[14],"$\\mathbb{Z}_m\\wr":[15],"S_n=(\\mathbb{Z}_m)^n\\rtimes":[16],"S_n$":[17],"generated":[18],"by":[19],"prefix":[21],"reversals.":[22],"In":[23],"this":[24],"paper,":[25],"we":[26,92,125],"establish":[27,94],"that,":[28,110],"for":[29,56,111],"all":[30],"$m,n\\geq2$,":[31],"spectral":[33,141],"gap":[34],"$\u03b3(P(m,n))$":[35,60,96],"normalized":[38],"Laplacian":[39],"satisfies":[40],"$\u03b1_m/n\\leq\u03b3(P(m,n))\\leq1/n$,":[41],"where":[42],"$\u03b1_m$":[43],"a":[45,54,73,82,103,127,130],"positive":[46],"constant":[47],"that":[48,95],"depends":[49],"only":[50],"on":[51],"$m$.":[52],"As":[53],"consequence,":[55],"every":[57],"fixed":[58,90,112],"$m\\geq2$,":[59],"$\u0398_m(1/n)$":[62],"as":[63,99],"$n\\to\\infty$.":[64],"proof":[66],"combines":[67],"Cesi's":[68],"semi-recursive":[69],"spectral-gap":[70],"inequality":[71],"with":[72,81],"Fourier":[74],"decomposition":[75],"appropriate":[78],"operators":[79],"associated":[80,150],"coset":[83,151],"Schreier":[84,152],"color-position":[87],"pairs.":[88],"For":[89],"$n\\geq2$,":[91],"also":[93],"$\u0398_n(m^{-2})$":[98],"$m\\to\\infty$.":[100],"This":[101],"disproves":[102],"conjecture":[104,132],"Blanco":[106],"and":[107,135,148],"Buehrle":[108],"asserting":[109],"$n$,":[113],"corresponding":[115],"undirected":[116],"graphs":[119],"form":[120],"an":[121],"expander":[122],"family.":[123],"Additionally,":[124],"present":[126],"counterexample":[128],"to":[129],"recent":[131],"Greaves":[134],"Zhu":[136],"concerning":[137],"equality":[138],"between":[139],"gaps":[142],"full":[145],"graph.":[153]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-08-19T00:00:00"}
