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Binary Sequences Generated by Sequences {n}, n = 1, 2, . .
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SYSNO ASEP 0344062 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Binary Sequences Generated by Sequences {n}, n = 1, 2, . . Author(s) Porubský, Štefan (UIVT-O) SAI, RID
Strauch, O. (SK)Source Title Publicationes Mathematicae-Debrecen. - : Kossuth Lajos Tudomanyegyetem - ISSN 0033-3883
Roč. 77, 1-2 (2010), s. 139-170Number of pages 32 s. Language eng - English Country HU - Hungary Keywords pseudorandomness ; binary sequence ; measures of pseudorandomness ; well distribution ; uniform distribution ; correlation ; Sturmian sequence Subject RIV BA - General Mathematics R&D Projects GA201/07/0191 GA ČR - Czech Science Foundation (CSF) CEZ AV0Z10300504 - UIVT-O (2005-2011) UT WOS 000279796100011 EID SCOPUS 77954902357 Annotation In the paper arithmetical and pseudorandom properties of the set A of fractional parts of multiplies of an irrational number which belong to a given subinterval of the unit interval (0,1) are studied. It is proved here that the gaps between successive elements of A are at most of three lengths, a, b and a+b, which extends the known Slater's results to arbitrary intervals. From the other results, let us mention the exact description of the set of integers which are not equal to a difference of two arbitrary elements of A, or a new lower estimate of the Mauduit-Sarkozy well distribution measure, or a new proof of the mentioned Slater’s three gap theorems. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2011
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