Let (Gn(x))n=0 be a d-th order linear recurrence sequence having polynomial characteristic roots, one of which has degree strictly greater than the others. Moreover, letm ≥ 2 be a given integer. We ask for n ∈ N such that the equation Gn(x) = g ◦ h is satisfied for a polynomial g ∈ C[x] with deg g = m and some polynomial h ∈ C[x]with degh > 1. We prove that for all but finitely many n these decompositions can be described in “finite terms” coming from a generic decomposition parameterized by an algebraic variety. All data in this description will be shown to be effectively computable.
{"title":"Composite values of polynomial power sums","authors":"C. Fuchs, C. Karolus","doi":"10.5802/ambp.380","DOIUrl":"https://doi.org/10.5802/ambp.380","url":null,"abstract":"Let (Gn(x))n=0 be a d-th order linear recurrence sequence having polynomial characteristic roots, one of which has degree strictly greater than the others. Moreover, letm ≥ 2 be a given integer. We ask for n ∈ N such that the equation Gn(x) = g ◦ h is satisfied for a polynomial g ∈ C[x] with deg g = m and some polynomial h ∈ C[x]with degh > 1. We prove that for all but finitely many n these decompositions can be described in “finite terms” coming from a generic decomposition parameterized by an algebraic variety. All data in this description will be shown to be effectively computable.","PeriodicalId":52347,"journal":{"name":"Annales Mathematiques Blaise Pascal","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71239917","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}
We give a counterexample to show that the quantum isometry group of a deformed finite dimensional spectral triple may not be isomorphic with a deformation of the quantum isometry group of the undeformed spectral triple.
{"title":"Quantum Isometry Group of Deformation: A Counterexample","authors":"Debashish Goswami, A. Mandal","doi":"10.5802/ambp.382","DOIUrl":"https://doi.org/10.5802/ambp.382","url":null,"abstract":"We give a counterexample to show that the quantum isometry group of a deformed finite dimensional spectral triple may not be isomorphic with a deformation of the quantum isometry group of the undeformed spectral triple.","PeriodicalId":52347,"journal":{"name":"Annales Mathematiques Blaise Pascal","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71239970","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}
Consider an open domain D on the plane, whose isoperimetric deficit is smaller than 1. This note shows that the difference between the barycenter of D and the barycenter of its boundary is bounded above by a constant times the isoperimetric deficit to the power 1/4. This power can be improved to 1/2, when D is furthermore assumed to be a convex domain, in any Euclidean space of dimension larger than 2. Keywords: Isoperimetric inequality on the plane, isoperimetric deficit, boundary barycenter, convex domains, isoperimetric stability.
{"title":"Isoperimetric stability of boundary barycenters in the plane","authors":"L. Miclo","doi":"10.5802/AMBP.383","DOIUrl":"https://doi.org/10.5802/AMBP.383","url":null,"abstract":"Consider an open domain D on the plane, whose isoperimetric deficit is smaller than 1. This note shows that the difference between the barycenter of D and the barycenter of its boundary is bounded above by a constant times the isoperimetric deficit to the power 1/4. This power can be improved to 1/2, when D is furthermore assumed to be a convex domain, in any Euclidean space of dimension larger than 2. Keywords: Isoperimetric inequality on the plane, isoperimetric deficit, boundary barycenter, convex domains, isoperimetric stability.","PeriodicalId":52347,"journal":{"name":"Annales Mathematiques Blaise Pascal","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71240051","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}
Let $Gamma$ be a Coxeter graph, let $W$ be its associated Coxeter group, and let $G$ be a group of symmetries of $Gamma$.Recall that, by a theorem of H{'e}e and M"uhlherr, $W^G$ is a Coxeter group associated to some Coxeter graph $hat Gamma$.We denote by $Phi^+$ the set of positive roots of $Gamma$ and by $hat Phi^+$ the set of positive roots of $hat Gamma$.Let $E$ be a vector space over a field $K$ having a basis in one-to-one correspondence with $Phi^+$.The action of $G$ on $Gamma$ induces an action of $G$ on $Phi^+$, and therefore on $E$.We show that $E^G$ contains a linearly independent family of vectors naturally in one-to-one correspondence with $hat Phi^+$ and we determine exactly when this family is a basis of $E^G$.This question is motivated by the construction of Krammer's style linear representations for non simply laced Artin groups.
{"title":"Root systems, symmetries and linear representations of Artin groups","authors":"O. Geneste, Jean-Yves H'ee, L. Paris","doi":"10.5802/ambp.381","DOIUrl":"https://doi.org/10.5802/ambp.381","url":null,"abstract":"Let $Gamma$ be a Coxeter graph, let $W$ be its associated Coxeter group, and let $G$ be a group of symmetries of $Gamma$.Recall that, by a theorem of H{'e}e and M\"uhlherr, $W^G$ is a Coxeter group associated to some Coxeter graph $hat Gamma$.We denote by $Phi^+$ the set of positive roots of $Gamma$ and by $hat Phi^+$ the set of positive roots of $hat Gamma$.Let $E$ be a vector space over a field $K$ having a basis in one-to-one correspondence with $Phi^+$.The action of $G$ on $Gamma$ induces an action of $G$ on $Phi^+$, and therefore on $E$.We show that $E^G$ contains a linearly independent family of vectors naturally in one-to-one correspondence with $hat Phi^+$ and we determine exactly when this family is a basis of $E^G$.This question is motivated by the construction of Krammer's style linear representations for non simply laced Artin groups.","PeriodicalId":52347,"journal":{"name":"Annales Mathematiques Blaise Pascal","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42082656","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}
R esum e. Ces notes sont consacr ees a la construction des limites homotopiques, et plus g en eralement, des images directes cohomologiques dans une cat egorie de mod eles arbitraire admettant des petites limites projectives. En outre, la th eorie des d erivateurs de Grothendieck est introduite, a la fois en tant que motivation pour l’ etude de telles structures, et en tant qu’outil de d emonstration.
{"title":"Images directes cohomologiques dans les catégories de modèles","authors":"Denis-Charles Cisinski","doi":"10.5802/AMBP.174","DOIUrl":"https://doi.org/10.5802/AMBP.174","url":null,"abstract":"R esum e. Ces notes sont consacr ees a la construction des limites homotopiques, et plus g en eralement, des images directes cohomologiques dans une cat egorie de mod eles arbitraire admettant des petites limites projectives. En outre, la th eorie des d erivateurs de Grothendieck est introduite, a la fois en tant que motivation pour l’ etude de telles structures, et en tant qu’outil de d emonstration.","PeriodicalId":52347,"journal":{"name":"Annales Mathematiques Blaise Pascal","volume":"10 1","pages":"195-244"},"PeriodicalIF":0.0,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71239898","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}
Pub Date : 1981-01-01DOI: 10.3929/ETHZ-A-000147073
N. Wirth
{"title":"Pascal-S: A Subset and its Implementation","authors":"N. Wirth","doi":"10.3929/ETHZ-A-000147073","DOIUrl":"https://doi.org/10.3929/ETHZ-A-000147073","url":null,"abstract":"","PeriodicalId":52347,"journal":{"name":"Annales Mathematiques Blaise Pascal","volume":"1 1","pages":"199-259"},"PeriodicalIF":0.0,"publicationDate":"1981-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75873961","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}
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