Báo cáo toán học: "On some densities in the set of permutations" ppsx

... := L(t, m) ≍ log m. Here and in the sequel the symbol a ≍ b means a ≪ b and b ≪ a while the electronic journal of combinatorics 17 (2010), #R100 6 On some densities in the set of permutations Eugenijus ... nontrivial outside the region of classical large deviations. Further, we apply them by inserting into the equalities given in Proposition 1. The very idea go...

Ngày tải lên: 08/08/2014, 12:22

... and the weight 1 to the other 4r − 2 points. If there are no codewords among the 4r −2 points, then there must be two codewords among the four points with weight 1/2. Thus m = 1 in Theorem 3. The ... and that the two non-codewords in F(i, j) are in the lower-left and upper-right corners (in the other case, we just go up instead of going down in what follows: as expl...

Ngày tải lên: 07/08/2014, 15:22

... 15.  Finally, let us also consider the subgraph ˙ G × + of G × + defined as follows: The vertex -set of ˙ G × + is again the set of positive integers, and n joined to m if for some distinct x, ... large integers . Theorem 3.1. The graph G × + contains -bundles for arbitrarily large integers .Inpar- ticular, for any positive integer , the graph G × + contains subgraphs...

Ngày tải lên: 07/08/2014, 08:20

... r-th move the following properties hold: (i) P ∩ S = ∅; (ii) every edge of Breaker is incident with some vertex of P ∪ S; (iii) the edge connecting the endpoints of P is free. The proof of Lemma ... improves the upper bound given in [2] by 1, the proof is much more involved. Another problem we address in this paper, is that of determining the smallest n for which...

Ngày tải lên: 07/08/2014, 21:21

... v 1 ∈ √ m ˆ Q. Proof. Let C be a circuit in G (∞, (u/n) √ m) and let C ∗ be the circuit constructed by applying the mapping M to the vertices of the circuit C. Then by the above theorem, C ∗ is a circuit in the ... edges of G(∞, 1) cross in U(See [9]). Using these facts and the above lemma, we can give the following theorem. Theorem 3.2. Let m be a square-free positi...

Ngày tải lên: 08/08/2014, 01:20

... replace the o(n −7/2 ) error term in the asymptotic expansion of B(n)/n!withO(n −9/2 ln 19 n). The following extension of Theorem 1 (the case m = 3) giving a complete asymptotic expansion of I(n, ... real number. In this paper, we represent b(n, k) as a real trigonometric integral. We then use the method of Laplace to give a complete asymptotic expansion of this integra...

Ngày tải lên: 07/08/2014, 06:20

... code to the saillance code is not possible. Changing the right-maximal records to other kinds of records is not possible either. Theorem 1.3 Let f be one of the following eight kinds of permutation ... that i is a d escent index of σ if σ(i) > σ(i + 1). We let desi(σ) stand for the set of all descent indices of σ ∈ S n . The sum of descent indices is called the...

Ngày tải lên: 08/08/2014, 12:22

... 321 since σ has a subse- quence 642 order-i somorphic to 321. Notation 2 The set of permutations in S n (i.e. of length n) avoi ding pattern τ is denoted S n (τ). The set of permutations in S n containing ... S n containing pattern τ exactly r times is denoted S n (τ; r). In fact, in Example 1, 642 is the only occurrence of 321 in σ. In 1995, Noonan [3] enumerate...

Ngày tải lên: 08/08/2014, 14:23

Ngày tải lên: 05/08/2014, 15:21

Ngày tải lên: 05/08/2014, 15:20