منابع مشابه
Complex Hadamard Matrices and the Spectral Set Conjecture
By analyzing the connection between complex Hadamard matrices and spectral sets we prove the direction “spectral ⇒ tile” of the Sectral Set Conjecture for all sets A of size |A| ≤ 5 in any finite Abelian group. This result is then extended to the infinite grid Z for any dimension d, and finally to R. It was pointed out recently in [16] that the corresponding statement fails for |A| = 6 in the g...
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Fuglede’s conjecture [2] states that a set Ω ⊂ Rn tiles R by translations if and only if L(Ω) has an orthogonal basis of exponentials. We obtain new partial results supporting the conjecture in dimension 1. 1 The results A Borel set Ω ⊂ Rn of positive measure is said to tile Rn by translations if there is a discrete set T ⊂ Rn such that, up to sets of measure 0, the sets Ω+ t, t ∈ T, are disjoi...
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We study two problems related to the Small Set Expansion Conjecture [14]: the Maximum weight m′-edge cover (MWEC ) problem and the Fixed cost minimum edge cover (FCEC ) problem. In the MWEC problem, we are given an undirected simple graph G = (V,E) with integral vertex weights. The goal is to select a set U ⊆ V of maximum weight so that the number of edges with at least one endpoint in U is at ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2004
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-04-07403-9