{"id":"https://openalex.org/W7166555939","doi":"https://doi.org/10.48550/arxiv.2606.27776","title":"Constructions and Characterizations of $s$-Plateaued Partitions","display_name":"Constructions and Characterizations of $s$-Plateaued Partitions","publication_year":2026,"publication_date":"2026-06-26","ids":{"openalex":"https://openalex.org/W7166555939","doi":"https://doi.org/10.48550/arxiv.2606.27776"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.27776","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.27776","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.27776","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5139556645","display_name":"Jiaxin Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Jiaxin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074409589","display_name":"Yadi Wei","orcid":"https://orcid.org/0009-0008-8391-3548"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wei, Yadi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139626932","display_name":"Fang-Wei Fu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fu, Fang-Wei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139622205","display_name":"Jin Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Jin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5115602560","display_name":"Fulin Li","orcid":"https://orcid.org/0000-0001-8731-8828"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Fulin","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":false,"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/T11130","display_name":"Coding theory and cryptography","score":0.963699996471405,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.963699996471405,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.018200000748038292,"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/T10849","display_name":"Finite Group Theory Research","score":0.004399999976158142,"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/bent-molecular-geometry","display_name":"Bent molecular geometry","score":0.8090000152587891},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.6851999759674072},{"id":"https://openalex.org/keywords/vector-space","display_name":"Vector space","score":0.4406000077724457},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.42089998722076416},{"id":"https://openalex.org/keywords/partition-function","display_name":"Partition function (quantum field theory)","score":0.40380001068115234},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.32010000944137573}],"concepts":[{"id":"https://openalex.org/C138211643","wikidata":"https://www.wikidata.org/wiki/Q675211","display_name":"Bent molecular geometry","level":2,"score":0.8090000152587891},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7864000201225281},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.6851999759674072},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6021999716758728},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45840001106262207},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.4406000077724457},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.42089998722076416},{"id":"https://openalex.org/C2778401447","wikidata":"https://www.wikidata.org/wiki/Q7140637","display_name":"Partition function (quantum field theory)","level":2,"score":0.40380001068115234},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.32010000944137573},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.27549999952316284},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.2662000060081482},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.2587999999523163}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.27776","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.27776","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.27776","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.27776","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Bent":[0],"partitions":[1,127,135,161],"play":[2],"a":[3,39,98,107,176,218,253],"significant":[4],"role":[5],"in":[6,91,93],"constructing":[7],"bent":[8,29,130,141,254],"functions":[9,116,120],"and":[10,17,55,117,195,233],"have":[11],"rich":[12],"connections":[13],"with":[14,226],"coding":[15],"theory":[16],"combinatorics.":[18],"In":[19,124,132],"this":[20],"paper,":[21],"we":[22,205,245],"introduce":[23],"$s$-plateaued":[24,64,100,105,112,115,119,134,152,160,167,180,220,230],"partitions,":[25],"which":[26,80,163],"generalize":[27],"the":[28,51,145,213],"partitions.":[30,131,142],"Let":[31],"$\u0393=\\{A_{i},":[32,182],"1":[33,183,197],"\\leq":[34,36,184,186,198,200],"i":[35,185,199],"K\\}$":[37],"be":[38,122,263],"partition":[40,65,181,216,231,255],"of":[41,66,68,88,110,148,150,159,178,217,238,257,259],"$V_{n}^{(p)}$,":[42],"where":[43,188,240],"$V_{n}^{(p)}$":[44,67,258],"is":[45,61,97,190,228,237,242],"an":[46,63,104,151,179,229,248],"$n$-dimensional":[47],"vector":[48],"space":[49],"over":[50],"prime":[52],"field":[53],"$\\mathbb{F}_{p}$":[54],"$p":[56,209],"\\mid":[57],"K$.":[58,201],"Then":[59],"$\u0393$":[60,92,256],"called":[62],"depth":[69,260],"$K$":[70],"if":[71,208,232,235],"each":[72],"$p$-ary":[73,99,111,166,219],"function":[74,168,221],"$f:":[75,222],"V_{n}^{(p)}":[76,223],"\\rightarrow":[77,224],"\\mathbb{F}_{p}$":[78,84,225],"for":[79,162],"every":[81],"$j":[82],"\\in":[83],"has":[85,169],"exactly":[86],"$\\frac{K}{p}$":[87],"sets":[89],"$A_{i}$":[90,149],"its":[94],"preimage":[95,214],"set,":[96],"function.":[101],"By":[102],"using":[103],"partition,":[106],"large":[108],"number":[109],"functions,":[113],"vectorial":[114],"generalized":[118],"can":[121],"constructed.":[123],"particular,":[125],"$0$-plateaued":[126],"are":[128,136],"just":[129],"general,":[133],"much":[137],"more":[138],"complicated":[139],"than":[140],"We":[143,154,174],"analyze":[144],"possible":[146],"cardinality":[147],"partition.":[153],"give":[155,175],"some":[156],"explicit":[157],"constructions":[158],"any":[164],"generated":[165],"no":[170],"nonzero":[171],"linear":[172],"structure.":[173],"characterization":[177],"K\\}$,":[187],"$p$":[189],"odd,":[191],"$K":[192],"\\geq":[193,210],"5$":[194],"$-A_{i}=A_{i},":[196],"Based":[202],"on":[203,251],"which,":[204],"show":[206],"that":[207],"5$,":[211],"then":[212],"set":[215],"$f(x)=f(-x)$":[227],"only":[234],"$f$":[236],"$(p-1)$-form,":[239],"$n+s$":[241],"even.When":[243],"$s=0$,":[244],"partially":[246],"address":[247],"open":[249],"problem":[250],"whether":[252],"$p^{\\frac{n}{2}}$":[261],"must":[262],"obtained":[264],"from":[265],"spreads.":[266]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-06-30T00:00:00"}
