{"id":"https://openalex.org/W3175430125","doi":"https://doi.org/10.48550/arxiv.2106.10182","title":"Cyclic Shuffle Compatibility","display_name":"Cyclic Shuffle Compatibility","publication_year":2021,"publication_date":"2021-06-18","ids":{"openalex":"https://openalex.org/W3175430125","doi":"https://doi.org/10.48550/arxiv.2106.10182","mag":"3175430125"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2106.10182","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2106.10182","pdf_url":"https://arxiv.org/pdf/2106.10182","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2106.10182","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013956635","display_name":"Rachel Domagalski","orcid":"https://orcid.org/0000-0003-2457-9195","observed_orcids":["https://orcid.org/0000-0003-2457-9195"]},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Domagalski, Rachel","raw_affiliation_strings":["\u2002Michigan State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u2002Michigan State University","institution_ids":["https://openalex.org/I87216513"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012757181","display_name":"Jinting Liang","orcid":"https://orcid.org/0000-0001-7161-4403","observed_orcids":["https://orcid.org/0000-0001-7161-4403"]},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Liang, Jinting","raw_affiliation_strings":["\u2002Michigan State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u2002Michigan State University","institution_ids":["https://openalex.org/I87216513"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061589632","display_name":"Quinn Minnich","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Minnich, Quinn","raw_affiliation_strings":["\u2002Michigan State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u2002Michigan State University","institution_ids":["https://openalex.org/I87216513"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070369805","display_name":"Bruce E. Sagan","orcid":"https://orcid.org/0000-0001-7700-6353","observed_orcids":["https://orcid.org/0000-0001-7700-6353"]},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sagan, Bruce E.","raw_affiliation_strings":["\u2002Michigan State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u2002Michigan State University","institution_ids":["https://openalex.org/I87216513"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018389489","display_name":"Jamie Schmidt","orcid":"https://orcid.org/0000-0003-2070-1798","observed_orcids":["https://orcid.org/0000-0003-2070-1798"]},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Schmidt, Jamie","raw_affiliation_strings":["\u2002Michigan State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u2002Michigan State University","institution_ids":["https://openalex.org/I87216513"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044944038","display_name":"Alexander Sietsema","orcid":"https://orcid.org/0000-0003-2307-2747","observed_orcids":["https://orcid.org/0000-0003-2307-2747"]},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sietsema, Alexander","raw_affiliation_strings":["\u2002Michigan State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u2002Michigan State University","institution_ids":["https://openalex.org/I87216513"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I87216513"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":3,"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":1.0,"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":1.0,"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/T13500","display_name":"Probability and Statistical Research","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11428","display_name":"Advanced Mathematical Identities","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/permutations","display_name":"permutations","score":0.5730000138282776},{"id":"https://openalex.org/keywords/quasisymmetric-functions","display_name":"quasisymmetric functions","score":0.8560000061988831},{"id":"https://openalex.org/keywords/major-index","display_name":"major index","score":0.9589999914169312},{"id":"https://openalex.org/keywords/p-partitions","display_name":"P-partitions","score":0.8090000152587891},{"id":"https://openalex.org/keywords/permutation-statistics","display_name":"permutation statistics","score":0.5230000019073486}],"concepts":[{"id":"https://openalex.org/C2778648169","wikidata":"https://www.wikidata.org/wiki/Q967768","display_name":"Compatibility (geochemistry)","level":2,"score":0.7665594816207886},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3672747313976288},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.18991237878799438},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.06924083828926086}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2106.10182","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2106.10182","pdf_url":"https://arxiv.org/pdf/2106.10182","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.2106.10182","doi":"https://doi.org/10.48550/arxiv.2106.10182","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2106.10182","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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2106.10182","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2106.10182","pdf_url":"https://arxiv.org/pdf/2106.10182","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":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W2077309624","https://openalex.org/W2483535718","https://openalex.org/W2621368248","https://openalex.org/W2805725189","https://openalex.org/W2808458304","https://openalex.org/W2810920038","https://openalex.org/W2914659449","https://openalex.org/W2950624353","https://openalex.org/W2964325760","https://openalex.org/W3168046744"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2748952813","https://openalex.org/W2390255551","https://openalex.org/W2367511445","https://openalex.org/W2381930792","https://openalex.org/W2358901819","https://openalex.org/W745733672","https://openalex.org/W2983545107","https://openalex.org/W2389102290","https://openalex.org/W2390279801"],"abstract_inverted_index":{"Consider":[0],"a":[1,16,115,171],"permutation":[2],"p":[3,35,61],"to":[4,129,150,158],"be":[5,26],"any":[6],"finite":[7],"list":[8],"of":[9,29,31,48,60,83,98,110,118,125,169,174],"distinct":[10],"positive":[11],"integers.":[12],"A":[13],"statistic":[14],"is":[15,21,42,66,90,128],"function":[17],"St":[18,41,49],"whose":[19],"domain":[20],"all":[22],"permutations.":[23],"Let":[24],"S(p,q)":[25,51],"the":[27,46,58,84,93,96,167,175],"set":[28],"shuffles":[30,87],"two":[32],"disjoint":[33],"permutations":[34,149],"and":[36,57,62,73,80,105,131,161],"q.":[37,63],"We":[38,153,164],"say":[39],"that":[40],"shuffle":[43,134,144],"compatible":[44],"if":[45],"distribution":[47],"over":[50],"depends":[52],"only":[53],"on":[54,71],"St(p),":[55],"St(q),":[56],"lengths":[59],"This":[64],"notion":[65],"implicit":[67],"in":[68,91,95],"Stanley's":[69],"work":[70],"P-partitions":[72],"was":[74],"first":[75],"explicitly":[76],"studied":[77],"by":[78],"Gessel":[79],"Zhuang.":[81],"One":[82],"places":[85],"where":[86,114],"are":[88],"useful":[89],"describing":[92],"product":[94],"algebra":[97,109],"quasisymmetric":[99,112],"functions.":[100],"Recently":[101],"Adin,":[102],"Gessel,":[103],"Reiner,":[104],"Roichman":[106],"defined":[107],"an":[108],"cyclic":[111,116,133,151,159,162,172],"functions":[113],"version":[117],"shuffling":[119],"comes":[120],"into":[121],"play.":[122],"The":[123],"purpose":[124],"this":[126,156],"paper":[127],"define":[130],"study":[132],"compatibility.":[135],"In":[136],"particular,":[137],"we":[138],"show":[139],"how":[140],"one":[141],"can":[142],"lift":[143],"compatibility":[145],"results":[146],"for":[147],"(linear)":[148],"ones.":[152],"then":[154],"apply":[155],"result":[157],"descents":[160],"peaks.":[163],"also":[165],"discuss":[166],"problem":[168],"finding":[170],"analogue":[173],"major":[176],"index.":[177]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-09-26T08:19:03.415552","created_date":"2025-10-10T00:00:00"}