{"id":"https://openalex.org/W2951472640","doi":"https://doi.org/10.48550/arxiv.1701.05529","title":"On lattice path matroid polytopes: integer points and Ehrhart polynomial","display_name":"On lattice path matroid polytopes: integer points and Ehrhart polynomial","publication_year":2017,"publication_date":"2017-01-19","ids":{"openalex":"https://openalex.org/W2951472640","doi":"https://doi.org/10.48550/arxiv.1701.05529","mag":"2951472640"},"language":"en","primary_location":{"id":"pmh:oai:HAL:hal-01457185v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-01457185","pdf_url":"https://hal.science/hal-01457185v1/file/LPM-Ehrhart150117.pdf","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2017","raw_type":"info:eu-repo/semantics/preprint"},"volume":null,"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-01457185v1/file/LPM-Ehrhart150117.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057566451","display_name":"Kolja B. Knauer","orcid":"https://orcid.org/0000-0002-8151-2184","observed_orcids":["https://orcid.org/0000-0002-8151-2184"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I21491767","display_name":"Aix-Marseille Universit\u00e9","ror":"https://ror.org/035xkbk20","country_code":"FR","type":"education","lineage":["https://openalex.org/I21491767"]},{"id":"https://openalex.org/I4210115196","display_name":"Laboratoire d\u2019Informatique Fondamentale de Marseille","ror":"https://ror.org/022my8t07","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I143002897","https://openalex.org/I21491767","https://openalex.org/I4210114274","https://openalex.org/I4210115196","https://openalex.org/I4210142724","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Knauer, Kolja","raw_affiliation_strings":["Laboratoire d\u2019Informatique Fondamentale, Facult\u00e9 des Sciences de Luminy, Aix-Marseille Universit\u00e9 and CNRS, Marseille Cedex 9, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire d\u2019Informatique Fondamentale, Facult\u00e9 des Sciences de Luminy, Aix-Marseille Universit\u00e9 and CNRS, Marseille Cedex 9, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I21491767","https://openalex.org/I4210115196"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047487492","display_name":"Leonardo Mart\u00ednez-Sandoval","orcid":"https://orcid.org/0000-0002-5104-9635","observed_orcids":["https://orcid.org/0000-0002-5104-9635"]},"institutions":[{"id":"https://openalex.org/I124227911","display_name":"Ben-Gurion University of the Negev","ror":"https://ror.org/05tkyf982","country_code":"IL","type":"education","lineage":["https://openalex.org/I124227911"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Mart\u00ednez-Sandoval, Leonardo","raw_affiliation_strings":["Department of Computer Science, Faculty of Natural Sciences, Ben-Gurion University of the Negev, Beer Sheva, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Faculty of Natural Sciences, Ben-Gurion University of the Negev, Beer Sheva, Israel","institution_ids":["https://openalex.org/I124227911"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055119261","display_name":"Jorge L. Ram\u00edrez Alfons\u00edn","orcid":"https://orcid.org/0000-0002-0514-7525","observed_orcids":["https://orcid.org/0000-0002-0514-7525"]},"institutions":[{"id":"https://openalex.org/I19894307","display_name":"Universit\u00e9 de Montpellier","ror":"https://ror.org/051escj72","country_code":"FR","type":"education","lineage":["https://openalex.org/I19894307"]},{"id":"https://openalex.org/I4210142014","display_name":"Institut Montpelli\u00e9rain Alexander Grothendieck","ror":"https://ror.org/044kxby82","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I19894307","https://openalex.org/I4210141950","https://openalex.org/I4210142014"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Alfons\u00edn, Jorge Luis Ram\u00edrez","raw_affiliation_strings":["Institut Montpelli\u00e9rain Alexander Grothendieck, Universit\u00e9 de Montpellier, Montpellier Cedex, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut Montpelli\u00e9rain Alexander Grothendieck, Universit\u00e9 de Montpellier, Montpellier Cedex, France","institution_ids":["https://openalex.org/I19894307","https://openalex.org/I4210142014"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9994999766349792,"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":0.9994999766349792,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.00019999999494757503,"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/T12069","display_name":"Commutative Algebra and Its Applications","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/ehrhart-polynomials","display_name":"Ehrhart polynomials","score":0.8489999771118164},{"id":"https://openalex.org/keywords/lattice-points","display_name":"lattice points","score":0.8050000071525574},{"id":"https://openalex.org/keywords/matroid-polytopes","display_name":"matroid polytopes","score":0.796999990940094},{"id":"https://openalex.org/keywords/affine-equivalence","display_name":"affine equivalence","score":0.7260000109672546},{"id":"https://openalex.org/keywords/polygonal-paths","display_name":"polygonal paths","score":0.6470000147819519},{"id":"https://openalex.org/keywords/lattice-paths","display_name":"lattice paths","score":0.3490000069141388}],"concepts":[{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.8855316638946533},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.8426242470741272},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7282540798187256},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6142421364784241},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5650716423988342},{"id":"https://openalex.org/C142885752","wikidata":"https://www.wikidata.org/wiki/Q1252145","display_name":"Integer lattice","level":3,"score":0.5235105156898499},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.49548375606536865},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.47080859541893005},{"id":"https://openalex.org/C111034964","wikidata":"https://www.wikidata.org/wiki/Q5597156","display_name":"Graphic matroid","level":3,"score":0.45854002237319946},{"id":"https://openalex.org/C178621168","wikidata":"https://www.wikidata.org/wiki/Q16155113","display_name":"Oriented matroid","level":4,"score":0.4572358727455139},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3478483557701111},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15352675318717957},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07800176739692688},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"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/C56863137","wikidata":"https://www.wikidata.org/wiki/Q743139","display_name":"Half-integer","level":2,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:HAL:hal-01457185v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-01457185","pdf_url":"https://hal.science/hal-01457185v1/file/LPM-Ehrhart150117.pdf","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2017","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.1701.05529","doi":"https://doi.org/10.48550/arxiv.1701.05529","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1701.05529","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-01457185v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-01457185","pdf_url":"https://hal.science/hal-01457185v1/file/LPM-Ehrhart150117.pdf","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2017","raw_type":"info:eu-repo/semantics/preprint"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2951472640.pdf","grobid_xml":"https://content.openalex.org/works/W2951472640.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1491410076","https://openalex.org/W1872892901","https://openalex.org/W1964291804","https://openalex.org/W1977516206","https://openalex.org/W1978284489","https://openalex.org/W1989856656","https://openalex.org/W2024086619","https://openalex.org/W2044911987","https://openalex.org/W2044935944","https://openalex.org/W2051569187","https://openalex.org/W2058830040","https://openalex.org/W2093397547","https://openalex.org/W2108171485","https://openalex.org/W2189814335","https://openalex.org/W2499069110","https://openalex.org/W2963048153"],"related_works":["https://openalex.org/W1978795414","https://openalex.org/W1562841224","https://openalex.org/W2582894873","https://openalex.org/W3093668615","https://openalex.org/W1963746795","https://openalex.org/W2016957139","https://openalex.org/W2951472640","https://openalex.org/W2040455566","https://openalex.org/W4300630553","https://openalex.org/W4301139944"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3,37,55],"investigate":[4],"the":[5,29,32,76],"number":[6],"of":[7,13,22,31,50,61,66,75,81],"integer":[8],"points":[9,24],"lying":[10],"in":[11,28],"dilations":[12],"lattice":[14,33,40],"path":[15,34,41],"matroid":[16,42],"polytopes.":[17,52],"We":[18],"give":[19],"a":[20,48,64],"characterization":[21],"such":[23],"as":[25],"polygonal":[26],"paths":[27],"diagram":[30],"matroid.":[35],"Furthermore,":[36],"prove":[38],"that":[39],"polytopes":[43],"are":[44],"affinely":[45],"equivalent":[46],"to":[47],"family":[49],"distributive":[51],"As":[53],"applications":[54],"obtain":[56],"two":[57],"new":[58],"infinite":[59],"families":[60],"matroids":[62],"verifying":[63],"conjecture":[65],"De":[67],"Loera":[68],"et.~al.":[69],"and":[70],"present":[71],"an":[72],"explicit":[73],"formula":[74],"Ehrhart":[77],"polynomial":[78],"for":[79],"one":[80],"them.":[82]},"counts_by_year":[],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2025-10-10T00:00:00"}