Showing papers by "Zhi-Wei Sun published in 1999"
27 Jan 1999
TL;DR: In this paper, it was shown that if A forms a minimal m-cover of Z, then for any t = 1, --, k there is an at E [0, 1] such that for every r = 0, 1, * *, nt 1 there exists an I C {1, **, k} \ {t} for which [s,E. 1/ns] > m 1 and {Es1EI 1/n} = (at + r)/nt.
Abstract: Let A = {as +n,Z}k= 1 be a system of arithmetic sequences which forms an m-cover of Z (i.e. every integer belongs at least to m members of A). In this paper we show the following surprising properties of A: (a) For each J C {1, * * , k} there exist at least m subsets I of {1, * * , k} with I $ J such that sE . 1/ns EsEJ 1/ns E Z. (b) If A forms a minimal m-cover of Z, then for any t = 1, --, k there is an at E [0, 1) such that for every r = 0,1, * *, nt 1 there exists an I C {1, * * , k} \ {t} for which [s,E. 1/ns] > m 1 and {Es1EI 1/ns} = (at + r)/nt.
23 citations