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  • Bounding Selmer Groups for the Rankin–Selberg Convolution of Coleman Families
    Can. J. Math. (IF 0.881) Pub Date : 2020-07-17
    Andrew Graham; Daniel R. Gulotta; Yujie Xu

    Let f and g be two cuspidal modular forms and let ${\mathcal {F}}$ be a Coleman family passing through f, defined over an open affinoid subdomain V of weight space $\mathcal {W}$ . Using ideas of Pottharst, under certain hypotheses on f and g, we construct a coherent sheaf over $V \times \mathcal {W}$ that interpolates the Bloch–Kato Selmer group of the Rankin–Selberg convolution of two modular forms

  • Erratum: The Jiang–Su Absorption for Inclusions of Unital C*-algebras
    Can. J. Math. (IF 0.881) Pub Date : 2020-06-11
    Hiroyuki Osaka; Tamotsu Teruya

    We correct an error in the statement in a proposition and a theorem in Jiang–Su absorption for inclusions of unital C*-algebras. Canad. J. Math. 70(2018), 400–425. This error was found by Dr. M. Ali Asadi-Vasfi and communicated to the authors by N. Christopher Phillips of the University of Oregon, who also suggested the outline for the following correct proofs.

  • Données endoscopiques d’un groupe réductif connexe : applications d’une construction de Langlands
    Can. J. Math. (IF 0.881) Pub Date : 2020-05-15
    Bertrand Lemaire; Jean-Loup Waldspurger

    Soient $F$ un corps global, et $G$ un groupe réductif connexe défini sur $F$ . On prouve que si deux données endoscopiques de $G$ sont équivalentes en presque toute place de $F$ , alors elles sont équivalentes. Le résultat est encore vrai pour l’endoscopie (ordinaire) avec caractère. On donne aussi, pour $F$ global ou local et $G$ quasi-simple simplement connexe, une description des données endoscopiques

  • Isospectrality for Orbifold Lens Spaces
    Can. J. Math. (IF 0.881) Pub Date : 2019-08-27
    Naveed S. Bari; Eugenie Hunsicker

    We answer Mark Kac’s famous question, “Can one hear the shape of a drum?” in the positive for orbifolds that are 3-dimensional and 4-dimensional lens spaces; we thus complete the answer to this question for orbifold lens spaces in all dimensions. We also show that the coefficients of the asymptotic expansion of the trace of the heat kernel are not sufficient to determine the above results.

  • Newforms of Half-integral Weight: The Minus Space Counterpart
    Can. J. Math. (IF 0.881) Pub Date : 2019-10-31
    Ehud Moshe Baruch; Soma Purkait

    We study genuine local Hecke algebras of the Iwahori type of the double cover of $\operatorname{SL}_{2}(\mathbb{Q}_{p})$ and translate the generators and relations to classical operators on the space $S_{k+1/2}(\unicode[STIX]{x1D6E4}_{0}(4M))$ , $M$ odd and square-free. In [9] Manickam, Ramakrishnan, and Vasudevan defined the new space of $S_{k+1/2}(\unicode[STIX]{x1D6E4}_{0}(4M))$ that maps Hecke

  • Marginals with Finite Repulsive Cost
    Can. J. Math. (IF 0.881) Pub Date : 2019-05-07
    Ugo Bindini

    We consider a multimarginal transport problem with repulsive cost, where the marginals are all equal to a fixed probability $\unicode[STIX]{x1D70C}\in {\mathcal{P}}(\mathbb{R}^{d})$ . We prove that, if the concentration of $\unicode[STIX]{x1D70C}$ is less than $1/N$ , then the problem has a solution of finite cost. The result is sharp, in the sense that there exists $\unicode[STIX]{x1D70C}$ with concentration

  • Automatic Sequences and Generalised Polynomials
    Can. J. Math. (IF 0.881) Pub Date : 2019-06-13
    Jakub Byszewski; Jakub Konieczny

    We conjecture that bounded generalised polynomial functions cannot be generated by finite automata, except for the trivial case when they are ultimately periodic.

  • One-Level Density of Low-lying Zeros of Quadratic and Quartic Hecke $L$ -functions
    Can. J. Math. (IF 0.881) Pub Date : 2019-08-30
    Peng Gao; Liangyi Zhao

    In this paper we prove some one-level density results for the low-lying zeros of families of quadratic and quartic Hecke $L$ -functions of the Gaussian field. As corollaries, we deduce that at least 94.27% and 5%, respectively, of the members of the quadratic family and the quartic family do not vanish at the central point.

  • Orlicz Addition for Measures and an Optimization Problem for the $f$ -divergence
    Can. J. Math. (IF 0.881) Pub Date : 2019-07-16
    Shaoxiong Hou; Deping Ye

    This paper provides a functional analogue of the recently initiated dual Orlicz–Brunn–Minkowski theory for star bodies. We first propose the Orlicz addition of measures, and establish the dual functional Orlicz–Brunn–Minkowski inequality. Based on a family of linear Orlicz additions of two measures, we provide an interpretation for the famous $f$ -divergence. Jensen’s inequality for integrals is also

  • Primes Dividing Invariants of CM Picard Curves
    Can. J. Math. (IF 0.881) Pub Date : 2019-05-07
    Pınar Kılıçer; Elisa Lorenzo García; Marco Streng

    We give a bound on the primes dividing the denominators of invariants of Picard curves of genus 3 with complex multiplication. Unlike earlier bounds in genus 2 and 3, our bound is based, not on bad reduction of curves, but on a very explicit type of good reduction. This approach simultaneously yields a simplification of the proof and much sharper bounds. In fact, unlike all previous bounds for genus

  • On the Chow Ring of Cynk–Hulek Calabi–Yau Varieties and Schreieder Varieties
    Can. J. Math. (IF 0.881) Pub Date : 2019-09-03
    Robert Laterveer; Charles Vial

    This note is about certain locally complete families of Calabi–Yau varieties constructed by Cynk and Hulek, and certain varieties constructed by Schreieder. We prove that the cycle class map on the Chow ring of powers of these varieties admits a section, and that these varieties admit a multiplicative self-dual Chow–Künneth decomposition. As a consequence of both results, we prove that the subring

  • Almost Simplicial Polytopes: The Lower and Upper Bound Theorems
    Can. J. Math. (IF 0.881) Pub Date : 2019-05-21
    Eran Nevo; Guillermo Pineda-Villavicencio; Julien Ugon; David Yost

    We study $n$ -vertex $d$ -dimensional polytopes with at most one nonsimplex facet with, say, $d+s$ vertices, called almost simplicial polytopes. We provide tight lower and upper bound theorems for these polytopes as functions of $d,n$ , and $s$ , thus generalizing the classical Lower Bound Theorem by Barnette and the Upper Bound Theorem by McMullen, which treat the case where $s=0$ . We characterize

  • CJM volume 72 Issue 2 Cover and Front matter
    Can. J. Math. (IF 0.881) Pub Date : 2020-03-31


  • CJM volume 72 Issue 2 Cover and Back matter
    Can. J. Math. (IF 0.881) Pub Date : 2020-03-31


  • Steiner symmetry in the minimization of the first eigenvalue of a fractional eigenvalue problem with indefinite weight
    Can. J. Math. (IF 0.881) Pub Date : 2020-04-14
    Claudia Anedda; Fabrizio Cuccu; Silvia Frassu

    Let $\Omega \subset \mathbb {R}^N$ , $N\geq 2$ , be an open bounded connected set. We consider the fractional weighted eigenvalue problem $(-\Delta )^s u =\lambda \rho u$ in $\Omega $ with homogeneous Dirichlet boundary condition, where $(-\Delta )^s$ , $s\in (0,1)$ , is the fractional Laplacian operator, $\lambda \in \mathbb {R}$ and $ \rho \in L^\infty (\Omega )$ . We study weak* continuity, convexity

  • The Trace Form Over Cyclic Number Fields
    Can. J. Math. (IF 0.881) Pub Date : 2020-04-14
    Wilmar Bolaños; Guillermo Mantilla-Soler

    In the mid 80’s Conner and Perlis showed that for cyclic number fields of prime degree p the isometry class of integral trace is completely determined by the discriminant. Here we generalize their result to tame cyclic number fields of arbitrary degree. Furthermore, for such fields, we give an explicit description of a Gram matrix of the integral trace in terms of the discriminant of the field.

  • Factorization problems in complex reflection groups
    Can. J. Math. (IF 0.881) Pub Date : 2020-04-02
    Joel Brewster Lewis; Alejandro H. Morales

    We enumerate factorizations of a Coxeter element in a well-generated complex reflection group into arbitrary factors, keeping track of the fixed space dimension of each factor. In the infinite families of generalized permutations, our approach is fully combinatorial. It gives results analogous to those of Jackson in the symmetric group and can be refined to encode a notion of cycle type. As one application

  • Classifying spaces for étale algebras with generators
    Can. J. Math. (IF 0.881) Pub Date : 2020-03-30
    Abhishek Kumar Shukla; Ben Williams

    We construct a scheme $B(r; {\mathbb {A}}^n)$ such that a map $X \to B(r; {\mathbb {A}}^n)$ corresponds to a degree-n étale algebra on X equipped with r generating global sections. We then show that when $n=2$ , i.e., in the quadratic étale case, the singular cohomology of $B(r; {\mathbb {A}}^n)({\mathbb {R}})$ can be used to reconstruct a famous example of S. Chase and to extend its application to

  • Reflection of Willmore Surfaces with Free Boundaries
    Can. J. Math. (IF 0.881) Pub Date : 2020-03-11
    Ernst Kuwert; Tobias Lamm

    We study immersed surfaces in $${\mathbb R}^3$$ that are critical points of the Willmore functional under boundary constraints. The two cases considered are when the surface meets a plane orthogonally along the boundary and when the boundary is contained in a line. In both cases we derive weak forms of the resulting free boundary conditions and prove regularity by reflection.

  • On Restriction Estimates for the Zero Radius Sphere over Finite Fields
    Can. J. Math. (IF 0.881) Pub Date : 2020-02-27
    Alex Iosevich; Doowon Koh; Sujin Lee; Thang Pham; Chun-Yen Shen

    In this paper, we completely solve the $L^{2}\to L^{r}$ extension conjecture for the zero radius sphere over finite fields. We also obtain the sharp $L^{p}\to L^{4}$ extension estimate for non-zero radii spheres over finite fields, which improves the previous result of the first and second authors significantly.

  • Coisotropic Submanifolds in b-symplectic Geometry
    Can. J. Math. (IF 0.881) Pub Date : 2020-02-24
    Stephane Geudens; Marco Zambon

    We study coisotropic submanifolds of b-symplectic manifolds. We prove that b-coisotropic submanifolds (those transverse to the degeneracy locus) determine the b-symplectic structure in a neighborhood, and provide a normal form theorem. This extends Gotay’s theorem in symplectic geometry. Further, we introduce strong b-coisotropic submanifolds and show that their coisotropic quotient, which locally

  • Coxeter Diagrams and the Köthe’s Problem
    Can. J. Math. (IF 0.881) Pub Date : 2020-02-24
    Ziba Fazelpour; Alireza Nasr-Isfahani

    A ring $\unicode[STIX]{x1D6EC}$ is called right Köthe if every right $\unicode[STIX]{x1D6EC}$ -module is a direct sum of cyclic modules. In this paper, we give a characterization of basic hereditary right Köthe rings in terms of their Coxeter valued quivers. We also give a characterization of basic right Köthe rings with radical square zero. Therefore, we give a solution to Köthe’s problem in these

  • Extension Property and Universal Sets
    Can. J. Math. (IF 0.881) Pub Date : 2020-02-24
    Łukasz Kosiński; Włodzimierz Zwonek

    Motivated by works on extension sets in standard domains, we introduce a notion of the Carathéodory set that seems better suited for the methods used in proofs of results on characterization of extension sets. A special stress is put on a class of two-dimensional submanifolds in the tridisc that not only turns out to be Carathéodory but also provides examples of two-dimensional domains for which the

  • An Application of Spherical Geometry to Hyperkähler Slices
    Can. J. Math. (IF 0.881) Pub Date : 2020-02-24
    Peter Crooks; Maarten van Pruijssen

    This work is concerned with Bielawski’s hyperkähler slices in the cotangent bundles of homogeneous affine varieties. One can associate such a slice with the data of a complex semisimple Lie group  $G$ , a reductive subgroup $H\subseteq G$ , and a Slodowy slice $S\subseteq \mathfrak{g}:=\text{Lie}(G)$ , defining it to be the hyperkähler quotient of $T^{\ast }(G/H)\times (G\times S)$ by a maximal compact

  • Universal Alternating Semiregular Polytopes
    Can. J. Math. (IF 0.881) Pub Date : 2020-02-12
    B. Monson; Egon Schulte

    In the classical setting, a convex polytope is said to be semiregular if its facets are regular and its symmetry group is transitive on vertices. This paper continues our study of alternating semiregular abstract polytopes, which have abstract regular facets, still with combinatorial automorphism group transitive on vertices and with two kinds of regular facets occurring in an alternating fashion.

  • Boundedness of Differential Transforms for Heat Semigroups Generated by Schrödinger Operators
    Can. J. Math. (IF 0.881) Pub Date : 2020-02-12
    Zhang Chao; José L. Torrea

    In this paper we analyze the convergence of the following type of series $$\begin{eqnarray}T_{N}^{{\mathcal{L}}}f(x)=\mathop{\sum }_{j=N_{1}}^{N_{2}}v_{j}\big(e^{-a_{j+1}{\mathcal{L}}}f(x)-e^{-a_{j}{\mathcal{L}}}f(x)\big),\quad x\in \mathbb{R}^{n},\end{eqnarray}$$ where ${\{e^{-t{\mathcal{L}}}\}}_{t>0}$ is the heat semigroup of the operator ${\mathcal{L}}=-\unicode[STIX]{x1D6E5}+V$ with $\unicode[STIX]{x1D6E5}$

  • Generalized Beilinson Elements and Generalized Soulé Characters
    Can. J. Math. (IF 0.881) Pub Date : 2020-02-06
    Kenji Sakugawa

    The generalized Soulé character was introduced by H. Nakamura and Z. Wojtkowiak and is a generalization of Soulé’s cyclotomic character. In this paper, we prove that certain linear sums of generalized Soulé characters essentially coincide with the image of generalized Beilinson elements in K-groups under Soulé’s higher regulator maps. This result generalizes Huber–Wildeshaus’ theorem, which is a cyclotomic

  • The Chord Index, its Definitions, Applications, and Generalizations
    Can. J. Math. (IF 0.881) Pub Date : 2020-01-30
    Zhiyun Cheng

    In this paper, we study the chord index of virtual knots, which can be thought of as an extension of the chord parity. We show how to use the chord index to enhance the quandle coloring invariants. The notion of indexed quandle is introduced, which generalizes the quandle idea. Some applications of this new invariant is discussed. We also study how to define a generalized chord index via a fixed finite

  • On Extensions for Gentle Algebras
    Can. J. Math. (IF 0.881) Pub Date : 2020-01-28
    İlke Çanakçı; David Pauksztello; Sibylle Schroll

    We give a complete description of a basis of the extension spaces between indecomposable string and quasi-simple band modules in the module category of a gentle algebra.

  • Matrix Liberation Process II: Relation to Orbital Free Entropy
    Can. J. Math. (IF 0.881) Pub Date : 2020-01-28
    Yoshimichi Ueda

    We investigate the concept of orbital free entropy from the viewpoint of the matrix liberation process. We will show that many basic questions around the definition of orbital free entropy are reduced to the question of full large deviation principle for the matrix liberation process. We will also obtain a large deviation upper bound for a certain family of random matrices that is essential to define

  • Ideal Uniform Polyhedra in $\mathbb{H}^{n}$ and Covolumes of Higher Dimensional Modular Groups
    Can. J. Math. (IF 0.881) Pub Date : 2020-01-27
    Ruth Kellerhals

    Higher dimensional analogues of the modular group $\mathit{PSL}(2,\mathbb{Z})$ are closely related to hyperbolic reflection groups and Coxeter polyhedra with big symmetry groups. In this context, we develop a theory and dissection properties of ideal hyperbolic $k$ -rectified regular polyhedra, which is of independent interest. As an application, we can identify the covolumes of the quaternionic modular

  • Variation of Mixed Hodge Structures Associated to an Equisingular One-dimensional Family of Calabi-Yau Threefolds
    Can. J. Math. (IF 0.881) Pub Date : 2020-01-16
    Isidro Nieto-Baños; Pedro Luis del Angel-Rodriguez

    We study the variations of mixed Hodge structures (VMHS) associated with a pencil ${\mathcal{X}}$ of equisingular hypersurfaces of degree $d$ in $\mathbb{P}^{4}$ with only ordinary double points as singularities, as well as the variations of Hodge structures (VHS) associated with the desingularization of this family $\widetilde{{\mathcal{X}}}$ . The notion of a set of singular points being in homologically

  • Classification of Simple Cuspidal Modules Over a Lattice Lie Algebra of Witt Type
    Can. J. Math. (IF 0.881) Pub Date : 2020-01-13
    Y. Billig; K. Iohara

    Let $W_{\unicode[STIX]{x1D70B}}$ be the lattice Lie algebra of Witt type associated with an additive inclusion $\unicode[STIX]{x1D70B}:\mathbb{Z}^{N}{\hookrightarrow}\mathbb{C}^{2}$ with $N>1$ . In this article, the classification of simple $\mathbb{Z}^{N}$ -graded $W_{\unicode[STIX]{x1D70B}}$ -modules, whose multiplicities are uniformly bounded, is given.

  • On Intrinsic Quadrics
    Can. J. Math. (IF 0.881) Pub Date : 2019-01-09
    Anne Fahrner; Jürgen Hausen

    An intrinsic quadric is a normal projective variety with a Cox ring defined by a single quadratic relation. We provide explicit descriptions of these varieties in the smooth case for small Picard numbers. As applications, we figure out in this setting the Fano examples and (affirmatively) test Fujita’s freeness conjecture.

  • Eisenstein Series Arising from Jordan Algebras
    Can. J. Math. (IF 0.881) Pub Date : 2019-01-09
    Marcela Hanzer; Gordan Savin

    We describe poles and the corresponding residual automorphic representations of Eisenstein series attached to maximal parabolic subgroups whose unipotent radicals admit Jordan algebra structure.

  • CJM volume 72 Issue 1 Cover and Front matter
    Can. J. Math. (IF 0.881) Pub Date : 2020-01-02


  • CJM volume 72 Issue 1 Cover and Back matter
    Can. J. Math. (IF 0.881) Pub Date : 2020-01-02


  • On the Linearity of Order-isomorphisms
    Can. J. Math. (IF 0.881) Pub Date : 2020-01-03
    Bas Lemmens; Onno van Gaans; Hendrik van Imhoff

    A basic problem in the theory of partially ordered vector spaces is to characterise those cones on which every order-isomorphism is linear. We show that this is the case for every Archimedean cone that equals the inf-sup hull of the sum of its engaged extreme rays. This condition is milder than existing ones and is satisfied by, for example, the cone of positive operators in the space of bounded self-adjoint

  • Generalizations of Menchov–Rademacher Theorem and Existence of Wave Operators in Schrödinger Evolution
    Can. J. Math. (IF 0.881) Pub Date : 2019-12-20
    Sergey Denisov; Liban Mohamed

    We obtain generalizations of the classical Menchov–Rademacher theorem to the case of continuous orthogonal systems. These results are applied to show the existence of Moller wave operators in Schrödinger evolution.

  • LYZ Matrices and SL( $n$ ) Contravariant Valuations on Polytopes
    Can. J. Math. (IF 0.881) Pub Date : 2019-12-18
    Dan Ma; Wei Wang

    All SL( $n$ ) contravariant symmetric matrix valued valuations on convex polytopes in $\mathbb{R}^{n}$ are completely classified without any continuity assumptions. The general Lutwak–Yang–Zhang matrix is shown to be essentially the unique such valuation.

  • Nearly Parallel G2-structures with Large Symmetry Group
    Can. J. Math. (IF 0.881) Pub Date : 2019-12-16
    Fabio Podestà

    We prove the existence of a one-parameter family of nearly parallel G2-structures on the manifold $\text{S}^{3}\times \mathbb{R}^{4}$ , which are mutually non-isomorphic and invariant under the cohomogeneity one action of the group SU(2)3. This family connects the two locally homogeneous nearly parallel G2-structures that are induced by the homogeneous ones on the sphere S7.

  • Sector Analogue of the Gauss–Lucas Theorem
    Can. J. Math. (IF 0.881) Pub Date : 2019-12-12
    Blagovest Sendov; Hristo Sendov

    The classical Gauss–Lucas theorem states that the critical points of a polynomial with complex coefficients are in the convex hull of its zeros. This fundamental theorem follows from the fact that if all the zeros of a polynomial are in a half plane, then the same is true for its critical points. The main result of this work replaces the half plane with a sector as follows.

  • Maximal Inequalities of Noncommutative Martingale Transforms
    Can. J. Math. (IF 0.881) Pub Date : 2019-11-22
    Yong Jiao; Fedor Sukochev; Dejian Zhou

    In this paper, we investigate noncommutative symmetric and asymmetric maximal inequalities associated with martingale transforms and fractional integrals. Our proofs depend on some recent advances on algebraic atomic decomposition and the noncommutative Gundy decomposition. We also prove several fractional maximal inequalities.

  • On a Property of Harmonic Measure on Simply Connected Domains
    Can. J. Math. (IF 0.881) Pub Date : 2019-11-22
    Christina Karafyllia

    Let $D\subset \mathbb{C}$ be a domain with $0\in D$ . For $R>0$ , let $\widehat{\unicode[STIX]{x1D714}}_{D}(R)$ denote the harmonic measure of $D\cap \{|z|=R\}$ at $0$ with respect to the domain $D\cap \{|z|0$ . Thus, the arising question, first posed by Betsakos, is the following: Does there exist a positive constant $C$ such that for all simply connected domains $D$ with $0\in D$ and all $R>0$ ,

  • Products of Involutions of an Infinite-dimensional Vector Space
    Can. J. Math. (IF 0.881) Pub Date : 2019-11-15
    Clément de Seguins Pazzis

    We prove that every automorphism of an infinite-dimensional vector space over a field is the product of four involutions, a result that is optimal in the general case. We also characterize the automorphisms that are the product of three involutions. More generally, we study decompositions of automorphisms into three or four factors with prescribed split annihilating polynomials of degree  $2$ .

  • Topology of Gleason Parts in Maximal Ideal Spaces with no Analytic Discs
    Can. J. Math. (IF 0.881) Pub Date : 2019-11-15
    Alexander J. Izzo; Dimitris Papathanasiou

    We strengthen, in various directions, the theorem of Garnett that every $\unicode[STIX]{x1D70E}$ -compact, completely regular space $X$ occurs as a Gleason part for some uniform algebra. In particular, we show that the uniform algebra can always be chosen so that its maximal ideal space contains no analytic discs. We show that when the space $X$ is metrizable, the uniform algebra can be chosen so that

  • Simple Formulas for Constellations and Bipartite Maps with Prescribed Degrees
    Can. J. Math. (IF 0.881) Pub Date : 2019-11-12
    Baptiste Louf

    We obtain simple quadratic recurrence formulas counting bipartite maps on surfaces with prescribed degrees (in particular, $2k$ -angulations) and constellations. These formulas are the fastest known way of computing these numbers.

  • Relative Equivariant Motives and Modules
    Can. J. Math. (IF 0.881) Pub Date : 2019-11-08
    Baptiste Calmès; Alexander Neshitov; Kirill Zainoulline

    We introduce and study various categories of (equivariant) motives of (versal) flag varieties. We relate these categories with certain categories of parabolic (Demazure) modules. We show that the motivic decomposition type of a versal flag variety depends on the direct sum decomposition type of the parabolic module. To do this we use localization techniques of Kostant and Kumar in the context of generalized

  • $\text{SL}(n)$ Invariant Valuations on Super-Coercive Convex Functions
    Can. J. Math. (IF 0.881) Pub Date : 2019-10-25
    Fabian Mussnig

    All non-negative, continuous, $\text{SL}(n)$ , and translation invariant valuations on the space of super-coercive, convex functions on $\mathbb{R}^{n}$ are classified. Furthermore, using the invariance of the function space under the Legendre transform, a classification of non-negative, continuous, $\text{SL}(n)$ , and dually translation invariant valuations is obtained. In both cases, different functional

  • New Simple Lattices in Products of Trees and their Projections
    Can. J. Math. (IF 0.881) Pub Date : 2019-10-07
    Nicolas Radu

    Let $\unicode[STIX]{x1D6E4}\leqslant \text{Aut}(T_{d_{1}})\times \text{Aut}(T_{d_{2}})$ be a group acting freely and transitively on the product of two regular trees of degree $d_{1}$ and  $d_{2}$ . We develop an algorithm that computes the closure of the projection of $\unicode[STIX]{x1D6E4}$ on $\text{Aut}(T_{d_{t}})$ under the hypothesis that $d_{t}\geqslant 6$ is even and that the local action

  • The Erdős–Moser Sum-free Set Problem
    Can. J. Math. (IF 0.881) Pub Date : 2019-09-23
    Tom Sanders

    We show that there is an absolute $c>0$ such that if $A$ is a finite set of integers, then there is a set $S\subset A$ of size at least $\log ^{1+c}|A|$ such that the restricted sumset $\{s+s^{\prime }:s,s^{\prime }\in S\text{ and }s\neq s^{\prime }\}$ is disjoint from $A$ . (The logarithm here is to base $3$ .)

  • Automaticity and Invariant Measures of Linear Cellular Automata
    Can. J. Math. (IF 0.881) Pub Date : 2019-09-05
    Eric Rowland; Reem Yassawi

    We show that spacetime diagrams of linear cellular automata $\unicode[STIX]{x1D6F7}:\,\mathbb{F}_{p}^{\mathbb{Z}}\rightarrow \mathbb{F}_{p}^{\mathbb{Z}}$ with $(-p)$ -automatic initial conditions are automatic. This extends existing results on initial conditions that are eventually constant. Each automatic spacetime diagram defines a $(\unicode[STIX]{x1D70E},\unicode[STIX]{x1D6F7})$ -invariant subset

  • The Category of Ordered Bratteli Diagrams
    Can. J. Math. (IF 0.881) Pub Date : 2019-09-03
    Massoud Amini; George A. Elliott; Nasser Golestani

    A category structure for ordered Bratteli diagrams is proposed in which isomorphism coincides with the notion of equivalence of Herman, Putnam, and Skau. It is shown that the natural one-to-one correspondence between the category of Cantor minimal systems and the category of simple properly ordered Bratteli diagrams is in fact an equivalence of categories. This gives a Bratteli–Vershik model for factor

  • Maximal Operator for the Higher Order Calderón Commutator
    Can. J. Math. (IF 0.881) Pub Date : 2019-09-03
    Xudong Lai

    In this paper, we investigate the weighted multilinear boundedness properties of the maximal higher order Calderón commutator for the dimensions larger than two. We establish all weighted multilinear estimates on the product of the $L^{p}(\mathbb{R}^{d},w)$ space, including some peculiar endpoint estimates of the higher dimensional Calderón commutator.

  • Polynomials from Combinatorial $K$ -theory
    Can. J. Math. (IF 0.881) Pub Date : 2019-09-03
    Cara Monical; Oliver Pechenik; Dominic Searles

    We introduce two new bases of the ring of polynomials and study their relations to known bases. The first basis is the quasi-Lascoux basis, which is simultaneously both a $K$ -theoretic deformation of the quasi-key basis and also a lift of the $K$ -analogue of the quasi-Schur basis from quasi-symmetric polynomials to general polynomials. We give positive expansions of this quasi-Lascoux basis into

  • The Genus of a Random Bipartite Graph
    Can. J. Math. (IF 0.881) Pub Date : 2019-08-29
    Yifan Jing; Bojan Mohar

    Archdeacon and Grable (1995) proved that the genus of the random graph $G\in {\mathcal{G}}_{n,p}$ is almost surely close to $pn^{2}/12$ if $p=p(n)\geqslant 3(\ln n)^{2}n^{-1/2}$ . In this paper we prove an analogous result for random bipartite graphs in ${\mathcal{G}}_{n_{1},n_{2},p}$ . If $n_{1}\geqslant n_{2}\gg 1$ , phase transitions occur for every positive integer $i$ when $p=\unicode[STIX]{x

  • GCR and CCR Steinberg Algebras
    Can. J. Math. (IF 0.881) Pub Date : 2019-08-23
    Lisa O. Clark; Benjamin Steinberg; Daniel W. van Wyk

    Kaplansky introduced the notions of CCR and GCR $C^{\ast }$ -algebras, because they have a tractable representation theory. Many years later, he introduced the notions of CCR and GCR rings. In this paper we characterize when the algebra of an ample groupoid over a field is CCR and GCR. The results turn out to be exact analogues of the corresponding characterization of locally compact groupoids with

  • Cohomology of Modules Over $H$ -categories and Co- $H$ -categories
    Can. J. Math. (IF 0.881) Pub Date : 2019-08-06
    Mamta Balodi; Abhishek Banerjee; Samarpita Ray

    Let $H$ be a Hopf algebra. We consider $H$ -equivariant modules over a Hopf module category ${\mathcal{C}}$ as modules over the smash extension ${\mathcal{C}}\#H$ . We construct Grothendieck spectral sequences for the cohomologies as well as the $H$ -locally finite cohomologies of these objects. We also introduce relative $({\mathcal{D}},H)$ -Hopf modules over a Hopf comodule category ${\mathcal{D}}$

  • On the Combinatorics of Gentle Algebras
    Can. J. Math. (IF 0.881) Pub Date : 2019-07-29
    Thomas Brüstle; Guillaume Douville; Kaveh Mousavand; Hugh Thomas; Emine Yıldırım

    For $A$ a gentle algebra, and $X$ and $Y$ string modules, we construct a combinatorial basis for $\operatorname{Hom}(X,\unicode[STIX]{x1D70F}Y)$ . We use this to describe support $\unicode[STIX]{x1D70F}$ -tilting modules for $A$ . We give a combinatorial realization of maps in both directions realizing the bijection between support $\unicode[STIX]{x1D70F}$ -tilting modules and functorially finite torsion

  • Bounded Depth Ascending HNN Extensions and $\unicode[STIX]{x1D70B}_{1}$ -Semistability at infinity
    Can. J. Math. (IF 0.881) Pub Date : 2019-07-22
    Michael L. Mihalik

    A well-known conjecture is that all finitely presented groups have semistable fundamental groups at infinity. A class of groups whose members have not been shown to be semistable at infinity is the class ${\mathcal{A}}$ of finitely presented groups that are ascending HNN-extensions with finitely generated base. The class ${\mathcal{A}}$ naturally partitions into two non-empty subclasses, those that

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