{"id":"https://openalex.org/W1551679380","doi":"https://doi.org/10.37236/1340","title":"Lattice walks in $Z^d$ and permutations with no long ascending subsequences","display_name":"Lattice walks in $Z^d$ and permutations with no long ascending subsequences","publication_year":1997,"publication_date":"1997-11-17","ids":{"openalex":"https://openalex.org/W1551679380","doi":"https://doi.org/10.37236/1340","mag":"1551679380"},"language":"en","primary_location":{"id":"doi:10.37236/1340","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1340","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v5i1r2/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/v5i1r2/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050163260","display_name":"Ira M. Gessel","orcid":"https://orcid.org/0000-0003-1061-5095"},"institutions":[{"id":"https://openalex.org/I6902469","display_name":"Brandeis University","ror":"https://ror.org/05abbep66","country_code":"US","type":"education","lineage":["https://openalex.org/I6902469"]},{"id":"https://openalex.org/I36788626","display_name":"California University of Pennsylvania","ror":"https://ror.org/01spssf70","country_code":"US","type":"education","lineage":["https://openalex.org/I36788626"]},{"id":"https://openalex.org/I2801851002","display_name":"Harvard University Press","ror":"https://ror.org/006v7bf86","country_code":"US","type":"other","lineage":["https://openalex.org/I136199984","https://openalex.org/I2801851002"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ira Gessel","raw_affiliation_strings":["Brandeis University Harvard University University of Pennsylvania","University of Pennsylvania","Harvard University","Brandeis University"],"affiliations":[{"raw_affiliation_string":"Brandeis University Harvard University University of Pennsylvania","institution_ids":["https://openalex.org/I6902469"]},{"raw_affiliation_string":"University of Pennsylvania","institution_ids":["https://openalex.org/I36788626"]},{"raw_affiliation_string":"Harvard University","institution_ids":["https://openalex.org/I2801851002"]},{"raw_affiliation_string":"Brandeis University","institution_ids":["https://openalex.org/I6902469"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088064415","display_name":"Jonathan Weinstein","orcid":"https://orcid.org/0000-0001-8245-2067"},"institutions":[{"id":"https://openalex.org/I36788626","display_name":"California University of Pennsylvania","ror":"https://ror.org/01spssf70","country_code":"US","type":"education","lineage":["https://openalex.org/I36788626"]},{"id":"https://openalex.org/I6902469","display_name":"Brandeis University","ror":"https://ror.org/05abbep66","country_code":"US","type":"education","lineage":["https://openalex.org/I6902469"]},{"id":"https://openalex.org/I2801851002","display_name":"Harvard University Press","ror":"https://ror.org/006v7bf86","country_code":"US","type":"other","lineage":["https://openalex.org/I136199984","https://openalex.org/I2801851002"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jonathan Weinstein","raw_affiliation_strings":["Brandeis University Harvard University University of Pennsylvania","Brandeis University","Harvard University","University of Pennsylvania"],"affiliations":[{"raw_affiliation_string":"Brandeis University Harvard University University of Pennsylvania","institution_ids":["https://openalex.org/I6902469"]},{"raw_affiliation_string":"Brandeis University","institution_ids":["https://openalex.org/I6902469"]},{"raw_affiliation_string":"Harvard University","institution_ids":["https://openalex.org/I2801851002"]},{"raw_affiliation_string":"University of Pennsylvania","institution_ids":["https://openalex.org/I36788626"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112203336","display_name":"Herbert S. Wilf","orcid":null},"institutions":[{"id":"https://openalex.org/I6902469","display_name":"Brandeis University","ror":"https://ror.org/05abbep66","country_code":"US","type":"education","lineage":["https://openalex.org/I6902469"]},{"id":"https://openalex.org/I2801851002","display_name":"Harvard University Press","ror":"https://ror.org/006v7bf86","country_code":"US","type":"other","lineage":["https://openalex.org/I136199984","https://openalex.org/I2801851002"]},{"id":"https://openalex.org/I36788626","display_name":"California University of Pennsylvania","ror":"https://ror.org/01spssf70","country_code":"US","type":"education","lineage":["https://openalex.org/I36788626"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Herbert S. Wilf","raw_affiliation_strings":["Brandeis University Harvard University University of Pennsylvania","Harvard University","University of Pennsylvania","Brandeis University"],"affiliations":[{"raw_affiliation_string":"Brandeis University Harvard University University of Pennsylvania","institution_ids":["https://openalex.org/I6902469"]},{"raw_affiliation_string":"Harvard University","institution_ids":["https://openalex.org/I2801851002"]},{"raw_affiliation_string":"University of Pennsylvania","institution_ids":["https://openalex.org/I36788626"]},{"raw_affiliation_string":"Brandeis University","institution_ids":["https://openalex.org/I6902469"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5050163260"],"corresponding_institution_ids":["https://openalex.org/I2801851002","https://openalex.org/I36788626","https://openalex.org/I6902469"],"apc_list":null,"apc_paid":null,"fwci":2.5997,"has_fulltext":true,"cited_by_count":33,"citation_normalized_percentile":{"value":0.86523126,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"5","issue":"1","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":0.9998999834060669,"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":0.9998999834060669,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9975000023841858,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9883999824523926,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.8561844825744629},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8503434658050537},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8448522090911865},{"id":"https://openalex.org/keywords/subsequence","display_name":"Subsequence","score":0.7055377960205078},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5668169260025024},{"id":"https://openalex.org/keywords/combinatorial-proof","display_name":"Combinatorial proof","score":0.5350564122200012},{"id":"https://openalex.org/keywords/longest-increasing-subsequence","display_name":"Longest increasing subsequence","score":0.5218386054039001},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42468926310539246},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.12659543752670288},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.06863740086555481}],"concepts":[{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.8561844825744629},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8503434658050537},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8448522090911865},{"id":"https://openalex.org/C137877099","wikidata":"https://www.wikidata.org/wiki/Q1332977","display_name":"Subsequence","level":3,"score":0.7055377960205078},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5668169260025024},{"id":"https://openalex.org/C118539577","wikidata":"https://www.wikidata.org/wiki/Q3402784","display_name":"Combinatorial proof","level":2,"score":0.5350564122200012},{"id":"https://openalex.org/C170006305","wikidata":"https://www.wikidata.org/wiki/Q4183855","display_name":"Longest increasing subsequence","level":4,"score":0.5218386054039001},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42468926310539246},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.12659543752670288},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.06863740086555481},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/1340","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1340","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v5i1r2/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:10.1.1.46.7227","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.46.7227","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.emis.de/journals/EJC/Volume_5/../Volume_5/PDF/v5i1r2.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1340","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1340","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v5i1r2/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":[{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309636","display_name":"University of Minnesota","ror":"https://ror.org/03grvy078"},{"id":"https://openalex.org/F4320311089","display_name":"National Security Agency","ror":"https://ror.org/0047bvr32"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1551679380.pdf","grobid_xml":"https://content.openalex.org/works/W1551679380.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W196531003","https://openalex.org/W1560447213","https://openalex.org/W2014678176","https://openalex.org/W2050039992","https://openalex.org/W2053973191","https://openalex.org/W2057808121","https://openalex.org/W2089719844","https://openalex.org/W4235936977","https://openalex.org/W4240950518"],"related_works":["https://openalex.org/W3122601395","https://openalex.org/W2969919693","https://openalex.org/W2125120904","https://openalex.org/W4225868058","https://openalex.org/W2035123411","https://openalex.org/W2112772040","https://openalex.org/W2131191265","https://openalex.org/W4389489786","https://openalex.org/W1540010783","https://openalex.org/W2075403678"],"abstract_inverted_index":{"We":[0,68,81],"identify":[1],"a":[2,76,83,96,114],"set":[3],"of":[4,22,25,28,55,57,65,79,89,100,108],"$d!$":[5],"signed":[6],"points,":[7,10,38,46],"called":[8],"Toeplitz":[9,37,45],"in":[11,106],"${{Z}}^d$,":[12],"with":[13],"the":[14,20,23,32,40,53,118],"following":[15],"property:":[16],"for":[17],"every":[18],"$n&gt;0$,":[19],"excess":[21],"number":[24,41,54],"lattice":[26,109],"walks":[27],"$n$":[29],"steps,":[30],"from":[31],"origin":[33],"to":[34,42,49],"all":[35,43],"positive":[36],"over":[39],"negative":[44],"is":[47],"equal":[48],"${n\\choose":[50],"n/2}$":[51],"times":[52],"permutations":[56],"$\\{1,2,\\dots":[58],",n\\}$":[59],"that":[60,116],"contain":[61],"no":[62],"ascending":[63],"subsequence":[64],"length":[66],"$&gt;d$.":[67],"prove":[69],"this":[70],"first":[71],"by":[72,86,103],"generating":[73],"functions,":[74],"using":[75],"determinantal":[77],"theorem":[78,102],"Gessel.":[80],"give":[82,113],"second":[84],"proof":[85,99,115],"direct":[87],"construction":[88],"an":[90],"appropriate":[91],"involution.":[92],"The":[93],"latter":[94],"provides":[95],"purely":[97],"combinatorial":[98],"Gessel's":[101],"interpreting":[104],"it":[105],"terms":[107],"walks.":[110],"Finally":[111],"we":[112],"uses":[117],"Schensted":[119],"algorithm.":[120]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
