Canadian Journal of Mathematics最新文献

{"title":"Lattice points in slices of prisms","authors":"Luis Ferroni, Daniel McGinnis","doi":"10.4153/s0008414x24000233","DOIUrl":"https://doi.org/10.4153/s0008414x24000233","url":null,"abstract":"<p>We conduct a systematic study of the Ehrhart theory of certain slices of rectangular prisms. Our polytopes are generalizations of the hypersimplex and are contained in the larger class of polypositroids introduced by Lam and Postnikov; moreover, they coincide with polymatroids satisfying the strong exchange property up to an affinity. We give a combinatorial formula for all the Ehrhart coefficients in terms of the number of weighted permutations satisfying certain compatibility properties. This result proves that all these polytopes are Ehrhart positive. Additionally, via an extension of a result by Early and Kim, we give a combinatorial interpretation for all the coefficients of the <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240323085929717-0561:S0008414X24000233:S0008414X24000233_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$h^*$</span></span></img></span></span>-polynomial. All of our results provide a combinatorial understanding of the Hilbert functions and the <span>h</span>-vectors of all algebras of Veronese type, a problem that had remained elusive up to this point. A variety of applications are discussed, including expressions for the volumes of these slices of prisms as weighted combinations of Eulerian numbers; some extensions of Laplace’s result on the combinatorial interpretation of the volume of the hypersimplex; a multivariate generalization of the flag Eulerian numbers and refinements; and a short proof of the Ehrhart positivity of the independence polytope of all uniform matroids.</p>","PeriodicalId":501820,"journal":{"name":"Canadian Journal of Mathematics","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140299421","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":"ON TAU-TILTING SUBCATEGORIES","authors":"J. Asadollahi, S. Sadeghi, H. Treffinger","doi":"10.4153/s0008414x24000221","DOIUrl":"https://doi.org/10.4153/s0008414x24000221","url":null,"abstract":"","PeriodicalId":501820,"journal":{"name":"Canadian Journal of Mathematics","volume":"27 15","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140257644","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":"On the Ziv–Merhav Theorem beyond Markovianity I","authors":"Nicholas Barnfield, Raphael Grondin, Gaia Pozzoli, Renaud Raquépas","doi":"10.4153/s0008414x24000178","DOIUrl":"https://doi.org/10.4153/s0008414x24000178","url":null,"abstract":"","PeriodicalId":501820,"journal":{"name":"Canadian Journal of Mathematics","volume":"41 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140258481","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":"Thompson’s semigroup and the first Hochschild cohomology","authors":"Linzhe Huang","doi":"10.4153/s0008414x24000154","DOIUrl":"https://doi.org/10.4153/s0008414x24000154","url":null,"abstract":"<p>In this paper, we apply the theory of algebraic cohomology to study the amenability of Thompson’s group <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240320082257093-0036:S0008414X24000154:S0008414X24000154_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$mathcal {F}$</span></span></img></span></span>. We introduce the notion of unique factorization semigroup which contains Thompson’s semigroup <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240320082257093-0036:S0008414X24000154:S0008414X24000154_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$mathcal {S}$</span></span></img></span></span> and the free semigroup <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240320082257093-0036:S0008414X24000154:S0008414X24000154_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$mathcal {F}_n$</span></span></img></span></span> on <span>n</span> (<span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240320082257093-0036:S0008414X24000154:S0008414X24000154_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$geq 2$</span></span></img></span></span>) generators. Let <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240320082257093-0036:S0008414X24000154:S0008414X24000154_inline5.png\"><span data-mathjax-type=\"texmath\"><span>$mathfrak {B}(mathcal {S})$</span></span></img></span></span> and <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240320082257093-0036:S0008414X24000154:S0008414X24000154_inline6.png\"><span data-mathjax-type=\"texmath\"><span>$mathfrak {B}(mathcal {F}_n)$</span></span></img></span></span> be the Banach algebras generated by the left regular representations of <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240320082257093-0036:S0008414X24000154:S0008414X24000154_inline7.png\"><span data-mathjax-type=\"texmath\"><span>$mathcal {S}$</span></span></img></span></span> and <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240320082257093-0036:S0008414X24000154:S0008414X24000154_inline8.png\"><span data-mathjax-type=\"texmath\"><span>$mathcal {F}_n$</span></span></img></span></span>, respectively. We prove that all derivations on <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240320082257093-0036:S0008414X24000154:S0008414X24000154_inline9.png\"><span data-mathjax-type=\"texmath\">","PeriodicalId":501820,"journal":{"name":"Canadian Journal of Mathematics","volume":"38 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140198958","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":"A classification of anomalous actions through model action absorption","authors":"Sergio Girón Pacheco","doi":"10.4153/s0008414x2400018x","DOIUrl":"https://doi.org/10.4153/s0008414x2400018x","url":null,"abstract":"<p>We discuss a strategy for classifying anomalous actions through model action absorption. We use this to upgrade existing classification results for Rokhlin actions of finite groups on C<span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240329083149113-0880:S0008414X2400018X:S0008414X2400018X_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$^*$</span></span></img></span></span>-algebras, with further assuming a UHF-absorption condition, to a classification of anomalous actions on these C<span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240329083149113-0880:S0008414X2400018X:S0008414X2400018X_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$^*$</span></span></img></span></span>-algebras.</p>","PeriodicalId":501820,"journal":{"name":"Canadian Journal of Mathematics","volume":"121 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140584743","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":"Tangle equations, the Jones conjecture, slopes of surfaces in tangle complements, and q-deformed rationals – ERRATUM","authors":"Adam S. Sikora","doi":"10.4153/s0008414x24000208","DOIUrl":"https://doi.org/10.4153/s0008414x24000208","url":null,"abstract":"","PeriodicalId":501820,"journal":{"name":"Canadian Journal of Mathematics","volume":"7 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140260759","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":"Spectral theory of the invariant Laplacian on the disk and the sphere – a complex analysis approach","authors":"Michael Heins, Annika Moucha, Oliver Roth","doi":"10.4153/s0008414x2400021x","DOIUrl":"https://doi.org/10.4153/s0008414x2400021x","url":null,"abstract":"<p>The central theme of this paper is the holomorphic spectral theory of the canonical Laplace operator of the complement <img mimesubtype=\"png\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240320082628999-0285:S0008414X2400021X:S0008414X2400021X_inline1.png?pub-status=live\" type=\"\"> of the “complexified unit circle” <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240320082628999-0285:S0008414X2400021X:S0008414X2400021X_inline2.png\"><span data-mathjax-type=\"texmath\"><span>${(z,w) in widehat {{mathbb C}}^2 colon z cdot w = 1}$</span></span></img></span></span>. We start by singling out a distinguished set of holomorphic eigenfunctions on the bidisk in terms of hypergeometric <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240320082628999-0285:S0008414X2400021X:S0008414X2400021X_inline3.png\"><span data-mathjax-type=\"texmath\"><span>${}_2F_1$</span></span></img></span></span> functions and prove that they provide a spectral decomposition of every holomorphic eigenfunction on the bidisk. As a second step, we identify the maximal domains of definition of these eigenfunctions and show that these maximal domains naturally determine the fine structure of the eigenspaces. Our main result gives an intrinsic classification of all closed Möbius invariant subspaces of eigenspaces of the canonical Laplacian of <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240320082628999-0285:S0008414X2400021X:S0008414X2400021X_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$Omega $</span></span></img></span></span>. Generalizing foundational prior work of Helgason and Rudin, this provides a unifying complex analytic framework for the real-analytic eigenvalue theories of both the hyperbolic and spherical Laplace operators on the open unit disk resp. the Riemann sphere and, in particular, shows how they are interrelated with one another.</img></p>","PeriodicalId":501820,"journal":{"name":"Canadian Journal of Mathematics","volume":"105 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140198961","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":"Corrigendum: A certain structure of Artin groups and the isomorphism conjecture","authors":"S.K. Roushon","doi":"10.4153/s0008414x24000191","DOIUrl":"https://doi.org/10.4153/s0008414x24000191","url":null,"abstract":"<p>In this note, we give an alternate proof of the Farrell–Jones isomorphism conjecture for the affine Artin groups of type <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240320124148349-0086:S0008414X24000191:S0008414X24000191_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$widetilde B_n$</span></span></img></span></span>.</p>","PeriodicalId":501820,"journal":{"name":"Canadian Journal of Mathematics","volume":"122 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140198966","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":"The restricted quantum double of the Yangian","authors":"C. Wendlandt","doi":"10.4153/s0008414x24000142","DOIUrl":"https://doi.org/10.4153/s0008414x24000142","url":null,"abstract":"","PeriodicalId":501820,"journal":{"name":"Canadian Journal of Mathematics","volume":"8 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139960889","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":"Shi arrangements and low elements in affine Coxeter groups","authors":"Nathan Chapelier-Laget, Christophe Hohlweg","doi":"10.4153/s0008414x24000130","DOIUrl":"https://doi.org/10.4153/s0008414x24000130","url":null,"abstract":"<p>Given an affine Coxeter group <span>W</span>, the corresponding Shi arrangement is a refinement of the corresponding Coxeter hyperplane arrangements that was introduced by Shi to study Kazhdan–Lusztig cells for <span>W</span>. Shi showed that each region of the Shi arrangement contains exactly one element of minimal length in <span>W</span>. Low elements in <span>W</span> were introduced to study the word problem of the corresponding Artin–Tits (braid) group and turns out to produce automata to study the combinatorics of reduced words in <span>W</span>. In this article, we show, in the case of an affine Coxeter group, that the set of minimal length elements of the regions in the Shi arrangement is precisely the set of low elements, settling a conjecture of Dyer and the second author in this case. As a by-product of our proof, we show that the descent walls – the walls that separate a region from the fundamental alcove – of any region in the Shi arrangement are precisely the descent walls of the alcove of its corresponding low element.</p>","PeriodicalId":501820,"journal":{"name":"Canadian Journal of Mathematics","volume":"284 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140099801","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}