Báo cáo toán học: "On cycles in the coprime graph of integers1" docx

... proof of Theorem 2. 2.2 Proof of Theorem 3 Here we assume that s 2 ≥  2 n,thecases 1 ≥  2 nis similar. Denote by P r the product of the primes not exceeding r. The rough outline of the proof will ... denote the greatest common divisor and [a, b] the least common multiple of integers a, b. Consider the coprime graph on the integers. This is the graph whose v...

Ngày tải lên: 07/08/2014, 06:22

Ngày tải lên: 05/08/2014, 15:21

... 3 2 }). In the case where 2h + 3 is the maximum of the odd numbers, it is necessary that, at the end of the string of odd numbers, namely after the vertex labeled 1, there is the label 2h + 2. In other ... consequence of Lemmas 4.1, 4 .2 , 4.3, 4.4 while the second line follows fr om Lemma 4.5. Lemma 4.6 proves item (vi) of Theorem 2.1 thereby completing the pr...

Ngày tải lên: 08/08/2014, 12:22

... study of English as a lingua franca in teaching Chinese to speakers of other languages”) have been conducted on the teaching of Chinese to multilingual international students within China. In the ... concerning the exclusive use of Chinese concerned the building and maintenance of a Sinophone identity. The exclusive use of Chinese was regarded as sign of a pure...

Ngày tải lên: 20/06/2014, 21:20

Ngày tải lên: 05/08/2014, 09:46

Ngày tải lên: 05/08/2014, 15:20

... none of the four strings occur. In the other case, one number (b) precedes or is preceded by the other two. In the former case the strings 2) and 3) occur, in the latter 1) and 4), so again there ... and the number of descents due to these is the same in both columns. Depending on the shape of the letters of w and v in the tableau (for simplicity, we wi...

Ngày tải lên: 07/08/2014, 06:22

... number of cycles violate (b) because the parity of the number of cycles in the structure D chosen there must be opposite the parity of |S| so that the final structure will have an odd number of cycles. ... results to other families of structures that exhibit the same kind of discontinuities, by study- ing f(n, r) when “fixed points” is replaced by “components o...

Ngày tải lên: 07/08/2014, 07:21

... directed cycles. If G has at least one cycle, the minimum length of a cycle in G is called the girth of G, denoted g(G). On the other hand, if G contains no cycles, the girth of G is defined to be in nity. ... v)isanarcinG,wecallv the terminus of (u, v). Since the number of special arcs is less than the number of vertices with outdegree exactly 1 in any digraph...

Ngày tải lên: 07/08/2014, 07:21

... in  p+j−1 p−1  ways (the number of ordered partitions of j into p nonzero summands). The starting positions of these components in C 1 and C 2 (relative to the position of the first component) can be chosen in ... Classify the graphs H = C 1 ∪ C 2 according to the number of components p and edges j in the intersection graph H  =  V (C 1 )∩V (C 2 ),E(C 1 )∩...

Ngày tải lên: 07/08/2014, 08:20