The minimum of the antichains in the factor poset |
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| Authors: | Gerard J. Chang Fred H. Hao |
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| Affiliation: | (1) Department of Mathematics, National Central University, 32054 Chung-Li, Taiwan, Republic of China;(2) Institute of Information Science, Academia Sinica, Nankang, 11529 Taipei, Taiwan, Republic of China;(3) Department of Applied Mathematics, Feng Chia University, Tai-Chung, Taiwan, Republic of China |
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| Abstract: | ![]()
Denote g(m, n) the minimum of min A, where A is a subset of {1, 2, ..., m} of size n and there do not exist two distinct x and y in A such that x divides y. We use a method of poset to prove that g(m, n)=2i for positive integer i log3m and 1+s(m, i–1)1+s(m, i), where s(m, i) is the number of odd integers x such that m/3im.Research was supported by National Science Council of Republic of China under Grant NSC74-0201-M008d-02. |
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| Keywords: | 05App 06A10 |
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