Journal: Expositiones Mathematicae

Abbreviation

Expo. math.

Publisher

Elsevier

Journal Volumes

ISSN

0723-0869
1878-0792

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Publications1 - 7 of 7
  • Exact categories
    Item type: Journal Article
    Bühler, Theo (2010)
    Expositiones Mathematicae
  • Periodicity and decidability of translational tilings by rational polygonal sets
    Item type: Journal Article
    de Dios Pont, Jaume; Grebík, Jan; Greenfeld, Rachel; et al. (2024)
    Expositiones Mathematicae
    The periodic tiling conjecture asserts that if a region Σ ⊂ Rᵈ tiles Rᵈ by translations then it admits at least one fully periodic tiling. This conjecture is known to hold in R, and recently it was disproved in sufficiently high dimensions. In this paper, we study the periodic tiling conjecture for polygonal sets: bounded open sets in R² whose boundary is a finite union of line segments. We prove the periodic tiling conjecture for any polygonal tile whose vertices are rational. As a corollary of our argument, we also obtain the decidability of tilings by rational polygonal sets. Moreover, we prove that any translational tiling by a rational polygonal tile is weakly-periodic, i.e., can be partitioned into finitely many singly-periodic pieces.
  • Open book decompositions and stable Hamiltonian structures
    Item type: Journal Article
    Wendl, Chris (2010)
    Expositiones Mathematicae
  • Continued fractions of arithmetic sequences of quadratics
    Item type: Journal Article
    Aka, Menny (2020)
    Expositiones Mathematicae
    Let x be a quadratic irrational and let P be the set of prime numbers. We show the existence of an infinite set S⊂P such that the statistics of the period of the continued fraction expansions along the sequence px:p∈S approach the ‘normal’ statistics given by the Gauss–Kuzmin measure. Under the generalized Riemann hypothesis, we prove that there exist full density subsets S⊂P and T⊂N satisfying the same assertion. We give a rate of convergence in all cases. © 2019 Elsevier GmbH
  • Social choice and topology
    Item type: Journal Article
    Beno Eckmann (2004)
    Expositiones Mathematicae
  • Quadratic forms, compositions and triality over F-1
    Item type: Journal Article
    Knus, M. A.; Tignol, J. P. (2013)
    Expositiones Mathematicae
  • Infinitely many leaf-wise intersections on cotangent bundles
    Item type: Journal Article
    Albers, Peter; Frauenfelder, Urs (2012)
    Expositiones Mathematicae
Publications1 - 7 of 7