Related papers: A general inequality for packings of boxes
Tilings of a surface of negative Euler characteristic by n-gons with n\ge 7 is a finite problem. We develop the algorithm for finding all the tilings for fixed number of tiles and present the calculation for tilings of surfaces of small…
This paper introduces two tiles whose tilings form a one-parameter family of tilings which can all be seen as digitization of two-dimensional planes in the four-dimensional Euclidean space. This family contains the Ammann-Beenker tilings as…
We prove a rigorous inequality estimating the purity of a reduced density matrix of a composite quantum system in terms of cross-correlation of the same state and an arbitrary product state. Various immediate applications of our result are…
The recent high level of interest in weighted complex networks gives rise to a need to develop new measures and to generalize existing ones to take the weights of links into account. Here we focus on various generalizations of the…
Classification theory and the study of projective varieties which are covered by rational curves of minimal degrees naturally leads to the study of families of singular rational curves. Since families of arbitrarily singular curves are hard…
Packing problems have been of great interest in many diverse contexts for many centuries. The optimal packing of identical objects has been often invoked to understand the nature of low temperature phases of matter. In celebrated work,…
In this paper, we study the structure of the set of tilings produced by any given tile-set. For better understanding this structure, we address the set of finite patterns that each tiling contains. This set of patterns can be analyzed in…
In this paper we consider the computational complexity of uniformizing a domain with a given computable boundary. We give nontrivial upper and lower bounds in two settings: when the approximation of boundary is given either as a list of…
We compute the Cech cohomology with integer coefficients of one-dimensional tiling spaces arising from not just one, but several different substitutions, all acting on the same set of tiles. These calculations involve the introduction of a…
Clustering algorithms are an essential part of the unsupervised data science ecosystem, and extrinsic evaluation of clustering algorithms requires a method for comparing the detected clustering to a ground truth clustering. In a general…
Let T be a tile in the Cartesian plane made up of finitely many rectangles whose corners have rational coordinates and whose sides are parallel to the coordinate axes. This paper gives necessary and sufficient conditions for a square to be…
We investigate a new family of regions that is the universal generalization of three well-known region families in the field of enumeration of tilings: the quasi-regular hexagons, the semi-hexagons, and the halved hexagons. We prove a…
Various topics concerning the entanglement of composite quantum systems are considered with particular emphasis concerning the strict relations of such a problem with the one of attributing objective properties to the constituents. Most of…
After a historical discussion of classical uniformisation results for Riemann surfaces, of problems appearing in higher dimensions, and of uniformisation results for projective manifolds with trivial or ample canonical bundle, we introduce…
In this letter, we propose and experimentally test a quantumness criterion for single systems. The criterion is based on the violation of an already reported classical inequality. This inequality is expressed in terms of joint probabilities…
Hypercontractive inequalities are a useful tool in dealing with extremal questions in the geometry of high-dimensional discrete and continuous spaces. In this survey we trace a few connections between different manifestations of…
We study the generalization of Correlation Clustering which incorporates fairness constraints via the notion of fairlets. The corresponding Fair Correlation Clustering problem has been studied from several perspectives to date, but has so…
We prove combinatorially that the parity of the number of domino tilings of a region is equal to the parity of the number of domino tilings of a particular subregion. Using this result we can resolve the holey square conjecture. We…
Recent studies showed that hardness, a complex property, can be calculated using very simple approaches or even analytical formulae. These form the basis for evaluating controversial experimental results (as we illustrate for…
Some inequalities in 2-inner product spaces generalizing Bessel's result that are similar to the Boas-Bellman inequality from inner product spaces, are given. Applications for determinantal integral inequalities are also provided.