Binary Sequences Generated by Sequences {n}, n = 1, 2, . .

0344062 - ÚI 2011 RIV HU eng J - Článek v odborném periodiku
Porubský, Štefan - Strauch, O.
Binary Sequences Generated by Sequences {n}, n = 1, 2, . .
Publicationes Mathematicae-Debrecen. Roč. 77, 1-2 (2010), s. 139-170. ISSN 0033-3883
Grant CEP: GA ČR GA201/07/0191
Grant ostatní: VEGA(SK) 2/7138/27
Výzkumný záměr: CEZ:AV0Z10300504
Klíčová slova: pseudorandomness * binary sequence * measures of pseudorandomness * well distribution * uniform distribution * correlation * Sturmian sequence
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.568, rok: 2010

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.
Trvalý link: http://hdl.handle.net/11104/0186375