http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
The number of B<sub>3</sub>-sets of a given cardinality
Dellamonica, D.,Kohayakawa, Y.,Lee, S.J.,Rodl, V.,Samotij, W. Academic Press 2016 Journal of combinatorial theory. Series A Vol.142 No.-
<P>A set S of integers is a B-3-set if all the sums of the form a(1) a(2)+a(3), with a(1), a(2) and a(3) epsilon S and a(1) <= a(2) <= a(3), are distinct. We obtain asymptotic bounds for the number of B-3-sets of a given cardinality contained in the interval [n] = {1,...,n}. We use these results to estimate the maximum size of a B-3-set contained in a typical (random) subset of [n] of a given cardinality. These results confirm conjectures recently put forward by the authors [On the number of B-h-sets, Combin. Probab. Comput. 25 (2016), no. 1, 108-127]. (C) 2016 Elsevier Inc. All rights reserved.</P>
On the Number of <i>B<sub>h</sub></i>-Sets
DELLAMONICA Jr, DOMINGOS,KOHAYAKAWA, YOSHIHARU,LEE, SANG JUNE,RÖ,DL, VOJTĚ,CH,SAMOTIJ, WOJCIECH Cambridge University Press 2016 Combinatorics, probability & computing Vol.25 No.1
<P>A set <I>A</I> of positive integers is a <I>Bh-set</I> if all the sums of the form <I>a</I>1 + . . . + <I>ah</I>, with <I>a</I>1,. . .,<I>ah</I> ∈ <I>A</I> and <I>a</I>1 ⩽ . . . ⩽ <I>ah</I>, are distinct. We provide asymptotic bounds for the number of <I>Bh</I>-sets of a given cardinality contained in the interval [<I>n</I>] = {1,. . .,<I>n</I>}. As a consequence of our results, we address a problem of Cameron and Erdős (1990) in the context of <I>Bh</I>-sets. We also use these results to estimate the maximum size of a <I>Bh</I>-sets contained in a typical (random) subset of [<I>n</I>] with a given cardinality.</P>