Báo cáo toán học: "On the uniform generation of modular diagrams" potx

... and replace the insertion of step j(i) + 1 and the extraction at step (i − 1) by respective ∅-steps, and thereby obtain the ∗-tableau f(ϑ). We then remove the two ∅-steps and obtain the unique ... = |D σ m (µ m = ∅)| equals the number of weighted core of length m, i.e. the number of modular diag r ams of length n. Suppose now we only consider sampling paths of weig...

Ngày tải lên: 08/08/2014, 12:23

... 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

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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 ... understand the comodule category over the corresponding Hopf algebra. The pair (r, s), where r is the number of roots and s is the number of poles of P ∧ (t) (se...

Ngày tải lên: 06/08/2014, 05:20

... 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

... vertex. 2. The initial vertex of the next edge is v(j, ∓k). 3. Determine the direction of the next edge by the sign of the entry ∓k in list j and the direction of the preceding edge according to the ... combining the information about the direction of the first edge with the corresponding crossing yields a rule for the direction of the second edge. If...

Ngày tải lên: 07/08/2014, 08:20