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B h [ g ] sequences
Author(s) -
Cilleruelo Javier,
Jiménez-Urroz Jorge
Publication year - 2000
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300015758
Subject(s) - mathematics , combinatorics , sequence (biology) , upper and lower bounds , mathematical analysis , chemistry , biochemistry
New upper and lower bounds are given for F h ( g, N ), the maximum size of a B h [ g ] sequence contained in [1, N ]. It is proved that and thatF h ( g , N ) ⩽(3 h h ! g N )1 / h ,and that, for any ε > 0 and g > g ( ε, h ),F h ( g , N ) ⩾( ( 1 − ε )π 6h g N )1 / h + o ( N 1 / h) .