Results 1 to 10 of about 268 (44)
Undecidability of the Spectral Gap
Forum of Mathematics, Pi, 2022 We construct families of translationally invariant, nearest-neighbour Hamiltonians on a 2D square lattice of d-level quantum systems (d constant), for which determining whether the system is gapped or gapless is an undecidable problem.
Toby Cubitt +2 more
doaj +1 more source
Combinatorial and harmonic-analytic methods for integer tilings
Forum of Mathematics, Pi, 2022 A finite set of integers A tiles the integers by translations if $\mathbb {Z}$ can be covered by pairwise disjoint translated copies of A. Restricting attention to one tiling period, we have $A\oplus B=\mathbb {Z}_M$ for some $M\in \mathbb {N}$ and $B ...
Izabella Łaba, Itay Londner
doaj +1 more source
An aperiodic monotile that forces nonperiodicity through dendrites
Bulletin of the London Mathematical Society, Volume 52, Issue 5, Page 942-959, October 2020., 2020 Abstract We introduce a new type of aperiodic hexagonal monotile; a prototile that admits infinitely many tilings of the plane, but any such tiling lacks any translational symmetry. Adding a copy of our monotile to a patch of tiles must satisfy two rules that apply only to adjacent tiles. The first is inspired by the Socolar–Taylor monotile, but can be
Michael Mampusti, Michael F. Whittaker
wiley +1 more source
A generalised Euler–Poincaré formula for associahedra
Bulletin of the London Mathematical Society, Volume 51, Issue 1, Page 181-192, February 2019., 2019 Abstract We derive a formula for the number of flip‐equivalence classes of tilings of an n‐gon by collections of tiles of shape dictated by an integer partition λ. The proof uses the Euler–Poincaré formula; and the formula itself generalises the Euler–Poincaré formula for associahedra.
Karin Baur, Paul P. Martin
wiley +1 more source
Perfect colourings of isonemal fabrics by thin striping [PDF]
, 2010 Perfect colouring of isonemal fabrics by thin striping of warp and weft and the closely related topic of isonemal prefabrics that fall apart are reconsidered and their relation further explored.
R. S. D. THOMAS, Thomas
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On substitution tilings of the plane with n-fold rotational symmetry [PDF]
, 2014 A method is described for constructing, with computer assistance, planar substitution tilings that have n-fold rotational symmetry. This method uses as prototiles the set of rhombs with angles that are integer multiples of pi/n, and includes various ...
Maloney, Gregory R.
core +2 more sources
Determining All Universal Tilers
, 2011 A universal tiler is a convex polyhedron whose every cross-section tiles the plane. In this paper, we introduce a certain slight-rotating operation for cross-sections of pentahedra.
B. Grünbaum +5 more
core +1 more source
On a strong version of the Kepler conjecture
, 2011 We raise and investigate the following problem that one can regard as a very close relative of the densest sphere packing problem. If the Euclidean 3-space is partitioned into convex cells each containing a unit ball, how should the shapes of the cells ...
Bezdek +5 more
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Tilings, sub-tilings, and spectral sets on p-adic space
Open MathematicsIn this article, we provide a characterization of tilings, sub-tilings, and spectral sets on the pp-adic space Qpd{{\mathbb{Q}}}_{p}^{d}. Our methods are based on pp-adic distributions and pp-adic Fourier analysis. We also obtained a sufficient condition
Kadir Mamateli
doaj +1 more source
Tilings of Rectangular Regions by Rectangular Tiles: Counts Derived from Transfer Matrices [PDF]
, 2014 Step by step completion of a left-to-right tiling of a rectangular floor with tiles of a single shape starts from one edge of the floor, considers the possible ways of inserting a tile at the leftmost uncovered square, passes through a sequence of rugged
Mathar, Richard J.
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