{"id":"https://openalex.org/W1602172244","doi":"https://doi.org/10.37236/1580","title":"From a Polynomial Riemann Hypothesis to Alternating Sign Matrices","display_name":"From a Polynomial Riemann Hypothesis to Alternating Sign Matrices","publication_year":2001,"publication_date":"2001-10-24","ids":{"openalex":"https://openalex.org/W1602172244","doi":"https://doi.org/10.37236/1580","mag":"1602172244"},"language":"en","primary_location":{"id":"doi:10.37236/1580","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1580","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v8i1r36/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v8i1r36/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026125535","display_name":"\u00d6mer E\u011fecio\u01e7lu","orcid":"https://orcid.org/0000-0002-6070-761X"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"\u00d6mer E\u011fecio\u011flu","raw_affiliation_strings":["University of California,Santa Barbara,"],"affiliations":[{"raw_affiliation_string":"University of California,Santa Barbara,","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004671873","display_name":"Timothy Redmond","orcid":"https://orcid.org/0009-0006-2218-4789"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Timothy Redmond","raw_affiliation_strings":["Department of Computer Science University of California, Santa Barbara CA 93106","College of Creative Studies, University of California, Santa Barbara CA 93106","Network Associates Inc., 3965 Freedom Circle, Santa Clara, CA 95054"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science University of California, Santa Barbara CA 93106","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"College of Creative Studies, University of California, Santa Barbara CA 93106","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"Network Associates Inc., 3965 Freedom Circle, Santa Clara, CA 95054","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034791290","display_name":"Charles Ryavec","orcid":null},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Charles Ryavec","raw_affiliation_strings":["University of California,Santa Barbara,"],"affiliations":[{"raw_affiliation_string":"University of California,Santa Barbara,","institution_ids":["https://openalex.org/I154570441"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5026125535"],"corresponding_institution_ids":["https://openalex.org/I154570441"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":26,"citation_normalized_percentile":{"value":0.1129242,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"8","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9991999864578247,"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"}},{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear 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/mathematics","display_name":"Mathematics","score":0.8310177326202393},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.7006704211235046},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.6489772796630859},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6135095357894897},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5912026762962341},{"id":"https://openalex.org/keywords/orthogonality","display_name":"Orthogonality","score":0.5609844326972961},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5150349140167236},{"id":"https://openalex.org/keywords/riemann-hypothesis","display_name":"Riemann hypothesis","score":0.5040156245231628},{"id":"https://openalex.org/keywords/gramian-matrix","display_name":"Gramian matrix","score":0.4860439896583557},{"id":"https://openalex.org/keywords/sign","display_name":"Sign (mathematics)","score":0.4377296268939972},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.42074811458587646},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38663047552108765},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33637940883636475},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13507431745529175}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8310177326202393},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.7006704211235046},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.6489772796630859},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6135095357894897},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5912026762962341},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.5609844326972961},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5150349140167236},{"id":"https://openalex.org/C199479865","wikidata":"https://www.wikidata.org/wiki/Q205966","display_name":"Riemann hypothesis","level":2,"score":0.5040156245231628},{"id":"https://openalex.org/C77246614","wikidata":"https://www.wikidata.org/wiki/Q1409400","display_name":"Gramian matrix","level":3,"score":0.4860439896583557},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.4377296268939972},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.42074811458587646},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38663047552108765},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33637940883636475},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13507431745529175},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/1580","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1580","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v8i1r36/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.21.8872","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.21.8872","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.ucsb.edu/~omer/DOWNLOADABLE/RiemannASM01.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.25.5352","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.25.5352","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_8/PDF/v8i1r36.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1580","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1580","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v8i1r36/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1602172244.pdf","grobid_xml":"https://content.openalex.org/works/W1602172244.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W191192809","https://openalex.org/W948034686","https://openalex.org/W1484130161","https://openalex.org/W1484543240","https://openalex.org/W1909201467","https://openalex.org/W1966268321","https://openalex.org/W2005999031","https://openalex.org/W2014082748","https://openalex.org/W2026897841","https://openalex.org/W2060244141","https://openalex.org/W2164293239","https://openalex.org/W2953181589","https://openalex.org/W4403296764"],"related_works":["https://openalex.org/W4390355884","https://openalex.org/W2059318893","https://openalex.org/W2095582735","https://openalex.org/W1965698851","https://openalex.org/W834942123","https://openalex.org/W4232542516","https://openalex.org/W1967331680","https://openalex.org/W3176637561","https://openalex.org/W1587967017","https://openalex.org/W2016923379"],"abstract_inverted_index":{"This":[0,274,344],"paper":[1],"begins":[2],"with":[3,102,271,354,361,380],"a":[4,8,113,177,215,337,374],"brief":[5],"discussion":[6,28],"of":[7,10,19,21,52,54,63,69,73,119,141,161,191,241,243,256,266,288,291,309,314,321,330,340,364],"class":[9,308,339,345],"polynomial":[11,34,79,88],"Riemann":[12],"hypotheses,":[13],"which":[14,315],"leads":[15,30],"to":[16,31,78,112,219,252,383],"the":[17,50,61,103,106,117,122,133,139,148,162,189,196,199,205,223,233,239,244,253,257,317,322,347,350,378],"consideration":[18],"sequences":[20,80,89],"orthogonal":[22,56],"polynomials":[23,57],"and":[24,67,185,229,282],"3-term":[25,104,120],"recursions.":[26,84],"The":[27],"further":[29],"higher":[32,91],"order":[33,92],"recursions,":[35,105,144],"including":[36],"4-term":[37,83,107,143,171],"recursions":[38,93,108,121,172],"where":[39],"orthogonality":[40],"is":[41,130,135,165,174,187,209,227],"lost.":[42],"Nevertheless,":[43],"we":[44,145,213,230,283,325],"show":[45,146,326],"that":[46,60,94,132,147,168,194,232,327],"classical":[47,99,216],"results":[48],"on":[49],"nature":[51],"zeros":[53,62,123,158,197],"real":[55,66,179],"(i.":[58],"e.,":[59],"$p_n$":[64],"are":[65,156,334],"those":[68,72],"$p_{n+1}$":[70],"interleave":[71],"$p_n$)":[74],"may":[75],"be":[76,151,359],"extended":[77],"satisfying":[81,90],"certain":[82,178,328,362],"We":[85,203,293,302],"identify":[86],"specific":[87],"should":[95],"also":[96,210,303],"satisfy":[97],"this":[98,186,289],"result.":[100],"As":[101],"give":[109,250,284],"rise":[110,251],"naturally":[111],"linear":[114,225],"functional.":[115],"In":[116],"case":[118,140],"fall":[124],"nicely":[125],"into":[126],"place":[127],"when":[128,154,176,222,246],"it":[129],"known":[131],"functional":[134,149,226,245],"positive,":[136,228],"but":[137],"in":[138,279],"our":[142,170,192],"can":[150,357],"positive":[152],"even":[153],"there":[155],"non-real":[157],"among":[159],"some":[160],"polynomials.":[163],"It":[164],"interesting,":[166],"however,":[167],"for":[169],"positivity":[173],"guaranteed":[175],"parameter":[180],"$C$":[181],"satisfies":[182],"$C\\ge":[183,207],"3$,":[184],"exactly":[188,221],"condition":[190,206],"result":[193],"guarantees":[195],"have":[198],"aforementioned":[200],"interleaving":[201],"property.":[202],"conjecture":[204],"3$":[208,249],"necessary.":[211],"Next":[212],"used":[214],"determinant":[217],"criterion":[218],"find":[220],"associated":[224],"found":[231],"Hankel":[234,297,318,342,384],"determinants":[235,298,319],"$\\Delta_n$":[236,320],"formed":[237],"from":[238,377],"sequence":[240,259,290,313],"moments":[242],"$C":[247],"=":[248],"initial":[254],"values":[255],"integer":[258,310],"$1,":[260],"3,":[261],"26,":[262],"646,":[263],"45885,":[264],"\\cdots,$":[265],"Alternating":[267],"Sign":[268],"Matrices":[269],"(ASMs)":[270],"vertical":[272,355,381],"symmetry.":[273],"spurred":[275],"an":[276,305,306],"intense":[277],"interest":[278],"these":[280,296],"moments,":[281],"9":[285],"diverse":[286],"characterizations":[287],"moments.":[292,323],"then":[294],"specify":[295],"as":[299,373],"Macdonald-type":[300],"integrals.":[301],"provide":[304],"infinite":[307],"sequences,":[311],"each":[312],"gives":[316],"Finally":[324],"$n$-tuples":[329,363],"non-intersecting":[331],"lattice":[332,369],"paths":[333],"evaluated":[335],"by":[336],"related":[338],"special":[341],"determinants.":[343,385],"includes":[346],"$\\Delta_n$.":[348],"At":[349],"same":[351],"time,":[352],"ASMs":[353,379],"symmetry":[356,382],"readily":[358],"identified":[360],"osculating":[365],"paths.":[366],"These":[367],"two":[368],"path":[370],"models":[371],"appear":[372],"natural":[375],"bridge":[376]},"counts_by_year":[{"year":2022,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
