{"title":"The spine of the (T)-graph of the Hilbert scheme of points in the plane","authors":"Diane Maclagan, Rob Silversmith","doi":"10.5070/c64163834","DOIUrl":"https://doi.org/10.5070/c64163834","url":null,"abstract":"","PeriodicalId":514877,"journal":{"name":"Combinatorial Theory","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141708915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Resilience for tight Hamiltonicity","authors":"Peter Allen, Olaf Parczyk, Vincent Pfenninger","doi":"10.5070/c64163846","DOIUrl":"https://doi.org/10.5070/c64163846","url":null,"abstract":"","PeriodicalId":514877,"journal":{"name":"Combinatorial Theory","volume":"74 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141714854","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Refining trees of tangles in abstract separation systems: inessential parts","authors":"Sandra Albrechtsen","doi":"10.5070/c64163854","DOIUrl":"https://doi.org/10.5070/c64163854","url":null,"abstract":"","PeriodicalId":514877,"journal":{"name":"Combinatorial Theory","volume":"117 18","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141697066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Rowmotion on (m)-Tamari and biCambrian lattices","authors":"Colin Defant, James Lin","doi":"10.5070/c64163852","DOIUrl":"https://doi.org/10.5070/c64163852","url":null,"abstract":". Thomas and Williams conjectured that rowmotion acting on the rational ( a, b )-Tamari lattice has order a + b − 1. We construct an equivariant bijection that proves this conjecture when b ≡ 1 (mod a ); in fact, we determine the entire orbit structure of rowmotion in this case, showing that it exhibits the cyclic sieving phenomenon. We additionally show that the down-degree statistic is homomesic for this action. In a different vein, we consider the action of rowmotion on Barnard and Reading’s biCambrian lattices. Settling a different conjecture of Thomas and Williams, we prove that if c is a bipartite Coxeter element of a coincidental-type Coxeter group W , then the orbit structure of rowmotion on the c -biCambrian lattice is the same as the orbit structure of rowmotion on the lattice of order ideals of the doubled root poset of type W .","PeriodicalId":514877,"journal":{"name":"Combinatorial Theory","volume":"6 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141700441","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Generalized recursive atom ordering and equivalence to CL-shellability","authors":"Patricia Hersh, Grace Stadnyk","doi":"10.5070/c64163855","DOIUrl":"https://doi.org/10.5070/c64163855","url":null,"abstract":"","PeriodicalId":514877,"journal":{"name":"Combinatorial Theory","volume":"2018 46","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141706645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}