Result: A discrete Fourier kernel and Fraenkel's tiling conjecture
Title:
A discrete Fourier kernel and Fraenkel's tiling conjecture
Authors:
Source:
Acta Arithmetica. 118:283-304
Publication Status:
Preprint
Publisher Information:
Institute of Mathematics, Polish Academy of Sciences, 2005.
Publication Year:
2005
Subject Terms:
discrete Fourier transform, Mathematics - Number Theory, 11B50, Arithmetic progressions, 42A16, 11L99, Density, gaps, topology, 0102 computer and information sciences, 01 natural sciences, Fourier coefficients, Fourier series of functions with special properties, special Fourier series, perfect covering, Fraenkel's conjecture, Other combinatorial number theory, FOS: Mathematics, Mathematics - Combinatorics, Number Theory (math.NT), Combinatorics (math.CO), 0101 mathematics, Trigonometric and exponential sums (general theory), Beatty set, Combinatorial aspects of packing and covering
Document Type:
Academic journal
Article<br />Other literature type
File Description:
application/xml
Language:
English
ISSN:
1730-6264
0065-1036
0065-1036
DOI:
10.4064/aa118-3-4
DOI:
10.48550/arxiv.math/0407306
Access URL:
https://www.impan.pl/shop/publication/transaction/download/product/83355?download.pdf
http://arxiv.org/abs/math/0407306
https://arxiv.org/pdf/math/0407306
https://arxiv.org/abs/math/0407306
https://eudml.org/doc/278576
http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.bwnjournal-article-doi-10_4064-aa118-3-4
https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/acta-arithmetica/all/118/3/83355/a-discrete-fourier-kernel-and-fraenkel-s-tiling-conjecture
http://www.math.ucsd.edu/~ronspubs/05_02_fraenkel_tiling.pdf
https://core.ac.uk/display/2578675
http://arxiv.org/abs/math/0407306
https://arxiv.org/pdf/math/0407306
https://arxiv.org/abs/math/0407306
https://eudml.org/doc/278576
http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.bwnjournal-article-doi-10_4064-aa118-3-4
https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/acta-arithmetica/all/118/3/83355/a-discrete-fourier-kernel-and-fraenkel-s-tiling-conjecture
http://www.math.ucsd.edu/~ronspubs/05_02_fraenkel_tiling.pdf
https://core.ac.uk/display/2578675
Rights:
arXiv Non-Exclusive Distribution
Accession Number:
edsair.doi.dedup.....75424f3fb6cdfd7e82944e6aa1afa6a0
Database:
OpenAIRE
Further Information
The set B_{p,r}^q:=\{\floor{nq/p+r} \colon n\in Z \} with integers p, q, r) is a Beatty set with density p/q. We derive a formula for the Fourier transform \hat{B_{p,r}^q}(j):=\sum_{n=1}^p e^{-2 ��i j \floor{nq/p+r} / q}. A. S. Fraenkel conjectured that there is essentially one way to partition the integers into m>2 Beatty sets with distinct densities. We conjecture a generalization of this, and use Fourier methods to prove several special cases of our generalized conjecture.
24 pages, 6 figures (now with minor revisions and clarifications)