Báo cáo toán học: "On the automorphism group of integral circulant graphs" docx

... automorphism group of unitary Cayley graphs and answer the open question from [23] about the ratio of the size of the automorphism group of X n and the size of the group of a ffine automorphisms of X n . ... dividing n ′ . The classes C i permute under the automorphism f, and the size of the automorphism group of each class is given by Theor...

Ngày tải lên: 08/08/2014, 14:22

... from the first of these results that the domination number of G(n, p) is no larger the electronic journal of combinatorics 8 (2001), #R37 1 ≥ (log n)( n)p 2 ε 2 + n = (log n)( n)p 2 4 + n := C. Thechoiceofε ... concentration for the domination number D n of the subgraph G(n, p)ofG( + ,p), p fixed. Specifically, we shall prove Theorem 5 Consider the infinite random graph G( + ,...

Ngày tải lên: 07/08/2014, 06:22

... ρ n (A). There exists a similar connection between the possible basis orders for general finite groups G and the possible exponents of Cayley digraphs. Therefore, the problem of extending Theo- rem ... special case of a result of Lev [L], generalising an earlier result of Freiman [F], concerning the growth of sumsets of a large subset of an arithmetic progression of i...

Ngày tải lên: 08/08/2014, 12:22

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Ngày tải lên: 05/08/2014, 15:20

... > 0), which completes the proof.  Proof of Theorem 2.1. If EX 2 < ∞ then s 2 n → σ 2 a.s. Therefore, the theorem follows if we show that the conditional distribution of Y ∗ nN n converges ... replacing the unknown distribution by the empirical distribution of the data in the definition of the statistical function, and then resampling the data to obtain a Monte...

Ngày tải lên: 06/08/2014, 05:20

... =min 1ir m i , ˆm = 1 r  r i=1 m i . The proofs of the following theorems can be obtained similarly as the proofs of Theorem 6.20.1, Theorem 6.20.2 in [1], so we omit them here. Theorem 2. Assume that xF ... further that lim sup x,y→∞ H(x, y) x < 1 − λ ∗ , (2.2) Then every solution {x n } ∞ n=−m of (2.1) is bounded. Proof. The proof follows from applying the mean value t...

Ngày tải lên: 06/08/2014, 05:20

... element of M. The construction of the linear functional resembles the integral on the Hopf algebra H given in the previous section. In fact, using the same method as in the proof of Theorem 3.2 ... tensor power of V is also a comodule over E .The map R : V ⊗V −→ V ⊗V is a comodule map. The classification of E-comodules is done with the help of the action of...

Ngày tải lên: 06/08/2014, 05:20

... defined in the same way as in the proof of Lemma 1. Lemma 3 Let λ be the number of distinct pairs of elements of B having the same cyclic ordering of edges incident on an element of A  . Then, if ... drawing of some K 5,z and let t 0 be an element of the partite F with z elements and let T be the set of all elements of F having the same cyclic ordering of e...

Ngày tải lên: 07/08/2014, 07:21