{"id":"https://openalex.org/W2566019243","doi":"https://doi.org/10.37236/7375","title":"Slicings of Parallelogram Polyominoes: Catalan, Schr\u00f6der, Baxter, and Other Sequences","display_name":"Slicings of Parallelogram Polyominoes: Catalan, Schr\u00f6der, Baxter, and Other Sequences","publication_year":2019,"publication_date":"2019-07-19","ids":{"openalex":"https://openalex.org/W2566019243","doi":"https://doi.org/10.37236/7375","mag":"2566019243"},"language":"en","primary_location":{"id":"doi:10.37236/7375","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7375","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i3p13/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":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i3p13/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038014316","display_name":"Nicholas R. Beaton","orcid":"https://orcid.org/0000-0001-8220-3917"},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"University of Melbourne","ror":"https://ror.org/01ej9dk98","country_code":"AU","type":"education","lineage":["https://openalex.org/I165779595"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Nicholas R. Beaton","raw_affiliation_strings":["University of Melbourne"],"affiliations":[{"raw_affiliation_string":"University of Melbourne","institution_ids":["https://openalex.org/I165779595"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110181824","display_name":"Mathilde Bouvel","orcid":null},"institutions":[{"id":"https://openalex.org/I202697423","display_name":"University of Zurich","ror":"https://ror.org/02crff812","country_code":"CH","type":"education","lineage":["https://openalex.org/I202697423"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Mathilde Bouvel","raw_affiliation_strings":["University of Zurich"],"affiliations":[{"raw_affiliation_string":"University of Zurich","institution_ids":["https://openalex.org/I202697423"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091484790","display_name":"Veronica Guerrini","orcid":"https://orcid.org/0000-0001-8888-9243"},"institutions":[{"id":"https://openalex.org/I102064193","display_name":"University of Siena","ror":"https://ror.org/01tevnk56","country_code":"IT","type":"education","lineage":["https://openalex.org/I102064193"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Veronica Guerrini","raw_affiliation_strings":["University of Siena"],"affiliations":[{"raw_affiliation_string":"University of Siena","institution_ids":["https://openalex.org/I102064193"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018231504","display_name":"Simone Rinaldi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Simone Rinaldi","raw_affiliation_strings":["University of Sienna"],"affiliations":[{"raw_affiliation_string":"University of Sienna","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5038014316"],"corresponding_institution_ids":["https://openalex.org/I165779595"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01324717,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"26","issue":"3","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":0.9998000264167786,"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":0.9998000264167786,"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/T11567","display_name":"semigroups and automata theory","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T12162","display_name":"Cellular Automata and Applications","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/polyomino","display_name":"Polyomino","score":0.9080711603164673},{"id":"https://openalex.org/keywords/catalan-number","display_name":"Catalan number","score":0.8612638711929321},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8051981925964355},{"id":"https://openalex.org/keywords/parallelogram","display_name":"Parallelogram","score":0.7875993847846985},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7428553104400635},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.738660991191864},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4344088137149811},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42849820852279663},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.17408397793769836},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1320168375968933},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08769842982292175}],"concepts":[{"id":"https://openalex.org/C69919132","wikidata":"https://www.wikidata.org/wiki/Q1144819","display_name":"Polyomino","level":3,"score":0.9080711603164673},{"id":"https://openalex.org/C43929256","wikidata":"https://www.wikidata.org/wiki/Q270513","display_name":"Catalan number","level":2,"score":0.8612638711929321},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8051981925964355},{"id":"https://openalex.org/C53118041","wikidata":"https://www.wikidata.org/wiki/Q45867","display_name":"Parallelogram","level":3,"score":0.7875993847846985},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7428553104400635},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.738660991191864},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4344088137149811},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42849820852279663},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.17408397793769836},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1320168375968933},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08769842982292175},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/7375","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7375","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i3p13/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":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1511.04864","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1511.04864","pdf_url":"https://arxiv.org/pdf/1511.04864","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2566019243","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1511.04864","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1511.04864","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1511.04864","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":"article-journal"}],"best_oa_location":{"id":"doi:10.37236/7375","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7375","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i3p13/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":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/G1020765710","display_name":null,"funder_award_id":"DE170100186","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"},{"id":"https://openalex.org/G611870384","display_name":null,"funder_award_id":"grant","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"}],"funders":[{"id":"https://openalex.org/F4320310984","display_name":"Pacific Institute for the Mathematical Sciences","ror":"https://ror.org/04w49dw51"},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2566019243.pdf","grobid_xml":"https://content.openalex.org/works/W2566019243.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W636070063","https://openalex.org/W1927422331","https://openalex.org/W1978985258","https://openalex.org/W2038250522","https://openalex.org/W2067239301","https://openalex.org/W2086915432","https://openalex.org/W2146998892","https://openalex.org/W2165766451","https://openalex.org/W2165891825","https://openalex.org/W2256553136","https://openalex.org/W2963419264","https://openalex.org/W2992937527","https://openalex.org/W3049485457","https://openalex.org/W6600283948","https://openalex.org/W6607280908"],"related_works":["https://openalex.org/W3000071903","https://openalex.org/W2256553136","https://openalex.org/W3196136727","https://openalex.org/W2920737621","https://openalex.org/W3191831692","https://openalex.org/W2611531305","https://openalex.org/W2042632881","https://openalex.org/W2587815823","https://openalex.org/W2064254398","https://openalex.org/W105821837","https://openalex.org/W2289169217","https://openalex.org/W2201174638","https://openalex.org/W2609771569","https://openalex.org/W2950659266","https://openalex.org/W2951078172","https://openalex.org/W2045430869","https://openalex.org/W1882541734","https://openalex.org/W2952335458","https://openalex.org/W3127599226","https://openalex.org/W1981997210"],"abstract_inverted_index":{"We":[0,25],"provide":[1],"a":[2,54,63,71],"new":[3,64,72],"succession":[4,18,41],"rule":[5],"(i.e.":[6],"generating":[7,107],"tree)":[8],"associated":[9],"with":[10],"Schr\u00f6der":[11,27,48,55,65,73],"numbers,":[12],"that":[13,118],"interpolates":[14],"between":[15],"the":[16,88,92,103],"known":[17],"rules":[19],"for":[20,95,122],"Catalan":[21],"and":[22,28,70,91,102,115],"Baxter":[23,29,51,68,86],"numbers.":[24],"define":[26,80],"generalizations":[30],"of":[31,50,57,59,67,75,83,85],"parallelogram":[32],"polyominoes,":[33],"called":[34],"slicings,":[35,94],"which":[36],"grow":[37],"according":[38],"to":[39],"these":[40],"rules.":[42],"In":[43],"passing,":[44],"we":[45,79,116],"also":[46],"exhibit":[47],"subclasses":[49,84],"classes,":[52],"namely":[53],"subset":[56,66,74],"triples":[58],"non-intersecting":[60],"lattice":[61],"paths,":[62],"permutations,":[69],"mosaic":[76],"floorplans.":[77],"Finally,":[78],"two":[81],"families":[82],"slicings:":[87],"$m$-skinny":[89],"slicings":[90],"$m$-row-restricted":[93],"$m":[96],"\\in":[97],"\\mathbb{N}$.":[98],"Using":[99],"functional":[100],"equations":[101],"kernel":[104],"method,":[105],"their":[106],"functions":[108],"are":[109,120],"computed":[110],"in":[111],"some":[112],"special":[113],"cases,":[114],"conjecture":[117],"they":[119],"algebraic":[121],"any":[123],"$m$.":[124]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}