Zobrazeno 1 - 10
of 94
pro vyhledávání: '"Matolcsi, Mate"'
Coven and Meyerowitz formulated two conditions which have since been conjectured to characterize all finite sets that tile the integers by translation. By periodicity, this conjecture is reduced to sets which tile a finite cyclic group $\mathbb{Z}_M$
Externí odkaz:
http://arxiv.org/abs/2411.03854
It is possible to have a packing by translates of a cube that is maximal (i.e.\ no other cube can be added without overlapping) but does not form a tiling. In the long running analogy of packing and tiling to orthogonality and completeness of exponen
Externí odkaz:
http://arxiv.org/abs/2410.12387
The notion of weak tiling was a key ingredient in the proof of Fuglede's spectral set conjecture for convex bodies \cite{conv}, due to the fact that every spectral set tiles its complement weakly with a suitable Borel measure. In this paper we review
Externí odkaz:
http://arxiv.org/abs/2410.04948
Autor:
Matolcsi, Mate, Ruzsa, Imre Z.
Publikováno v:
Proceedings of the Steklov Institute of Mathematics 314 : 1 pp. 138-143, 6 p. (2021)
By constructing suitable nonnegative exponential sums we give upper bounds on the cardinality of any set $B_q$ in cyclic groups $\ZZ_q$ such that the difference set $B_q-B_q$ avoids cubic residues modulo $q$.
Comment: 8 pages
Comment: 8 pages
Externí odkaz:
http://arxiv.org/abs/2406.00406
We prove that the fractional chromatic number $\chi_f(\mathbb{R}^2)$ of the unit distance graph of the Euclidean plane is greater than or equal to $4$. A fundamental ingredient of the proof is the notion of geometric fractional chromatic number $\chi
Externí odkaz:
http://arxiv.org/abs/2311.10069
We discuss the relation of tiling, weak tiling and spectral sets in finite abelian groups. In particular, in elementary $p$-groups $(\mathbb{Z}_p)^d$, we introduce an averaging procedure that leads to a natural object of study: a 4-tuple of functions
Externí odkaz:
http://arxiv.org/abs/2212.05513
Publikováno v:
Sampling Theory, Signal Processing, and Data Analysis 21 (2023), Paper No. 31
A set $\Omega \subset \mathbb{R}^d$ is said to be spectral if the space $L^2(\Omega)$ admits an orthogonal basis of exponential functions. Fuglede (1974) conjectured that $\Omega$ is spectral if and only if it can tile the space by translations. Whil
Externí odkaz:
http://arxiv.org/abs/2209.04540
By improving upon previous estimates on a problem posed by L. Moser, we prove a conjecture of Erd\H{o}s that the density of any measurable planar set avoiding unit distances cannot exceed $1/4$. Our argument implies the upper bound of $0.2470$.
Externí odkaz:
http://arxiv.org/abs/2207.14179
Autor:
Matolcsi, Máté, Weiner, Mihály
Suppose that for some unit vectors $b_1,\ldots b_n$ in $\mathbb C^d$ we have that for any $j\neq k$ $b_j$ is either orthogonal to $b_k$ or $|\langle b_j,b_k\rangle|^2 = 1/d$ (i.e. $b_j$ and $b_k$ are unbiased). We prove that if $n=d(d+1)$, then these
Externí odkaz:
http://arxiv.org/abs/2112.00090
Autor:
Lev, Nir, Matolcsi, Máté
Publikováno v:
Acta Mathematica 228 (2022), no. 2, 385-420
A set $\Omega \subset \mathbb{R}^d$ is said to be spectral if the space $L^2(\Omega)$ has an orthogonal basis of exponential functions. A conjecture due to Fuglede (1974) stated that $\Omega$ is a spectral set if and only if it can tile the space by
Externí odkaz:
http://arxiv.org/abs/1904.12262