Related papers: Tilings by translation
In this paper we study algorithms for tiling problems. We show that the conditions $(T1)$ and $(T2)$ of Coven and Meyerowitz, conjectured to be necessary and sufficient for a finite set $A$ to tile the integers, can be checked in time…
Machine Translation (MT) has been widely used for cross-lingual classification, either by translating the test set into English and running inference with a monolingual model (translate-test), or translating the training set into the target…
Although more and more language pairs are covered by machine translation services, there are still many pairs that lack translation resources. Cross-language information retrieval (CLIR) is an application which needs translation…
In this paper we describe how the translation methodology adopted for the Spoken Language Translator (SLT) addresses the characteristics of the speech translation task in a context where it is essential to achieve easy customization to new…
The cohomology of a tiling or a point pattern has originally been defined via the construction of the hull or the groupoid associated with the tiling or the pattern. Here we present a construction which is more direct and therefore easier…
In this article, we study translations between variants of defaults logics such that the extensions of the theories that are the input and the output of the translation are in a bijective correspondence. We assume that a translation can…
In the present article, the author uses Fourier theory of tempered distributions (generalized functions) in deriving a formula for Dirichlet-like integrals. The applied method is remarkably efficient and allows a solution in a few…
Machine Translation (MT) tools are widely used today, often in contexts where professional translators are not present. Despite progress in MT technology, a gap persists between system development and real-world usage, particularly for…
We define a convolution operation on the set of polyominoes and use it to obtain a criterion for a given polyomino not to tile the plane (rotations and translations allowed). We apply the criterion to several families of polyominoes, and…
Moir\'e patterns of twisted and scaled bilayers have recently emerged as a fertile source of quasiperiodic order in two-dimensional materials. Inspired by these systems, we introduce the \emph{near-coincidence method} for generating…
In a recent paper, Byun presented nice formulas for the enumeration of lozenge tilings of certain hexagonal regions with intrusions. This paper attempts to generalise some of Byun's investigations.
Permutation polynomials with explicit constructions over finite fields have long been a topic of great interest in number theory. In recent years, by applying linear translators of functions from $\mathbb{F}_{q^n}$ to $\mathbb{F}_q$, many…
A tiling is a decomposition of a polygon into finitely many non-overlapping triangles. We prove that if a regular n-gon, $n \geq 5$, $n \neq 28$, can be tiled with similar right triangles, then one of the angles of these triangles is in…
This paper deals with continuous and compact mappings of the Fourier transform in function spaces with dominating mixed smoothness.
The translation operator $T^A$ associated with the special affine Fourier transform (SAFT) $\mathscr{F}_A$ is introduced from harmonic analysis point of view. The analogues of Wendel's theorem, Wiener theorem, Weiner-Tauberian theorem and…
All simple translation-invariant valuations on polytopes are classified. As a direct consequence the well-known conditions for translative-equidecomposability are recovered. Furthermore, a simplified proof of the classification of…
In this document, we collected the most important complexity results of tilings. We also propose a definition of a so-called deterministic set of tile types, in order to capture deterministic classes without the notion of games. We also…
We investigate properties of tempered distributions with discrete or countable supports such that their Fourier transforms are distributions with discrete or countable supports as well. We find sufficient conditions for support of the…
Tilting modules, generalising the notion of progenerator, furnish equivalences between pieces of module categories. This paper is dedicated to study how much these pieces say about the whole category. We will survey the existing results in…
A combinatorial substitution is a map over tilings which allows to define sets of tilings with a strong hierarchical structure. In this paper, we show that such sets of tilings are sofic, that is, can be enforced by finitely many local…