Báo cáo toán học: "The spectral category and the Connes invariant $Gamma$ " ppt

... class="bi x1 y0 w3 h 2" alt =""

Ngày tải lên: 05/08/2014, 15:20

... largest in their equivalence class as standard trees, and use them as equivalence class representatives. We will de- note the set of standard Catalan trees by standard(C) and the set of standard marked ... by standard(C, ∗). The standard trees in C 4 are , , , , . One of the standard trees in CH 3 is . The standard tree representing the class [T ]isT . We will also say that [S...

Ngày tải lên: 07/08/2014, 06:22

... between the self-describing sequences and the Catalan family tree. Theorem 2. The full names of the members of the Catalan family are precisely the self- describing sequences. In other words, they ... statements of the theorem are implied by Theorem 1 and the following lemma. Lemma 1. If a is a member of the Catalan family then a = δa. Otherwise, a<δa. Proof. The pr...

Ngày tải lên: 07/08/2014, 07:21

... each, and other random variables. Equiprobable allocations are the most simple and well studied. Consider, for example, an Internet voting on the theme: “Which of the N teams will win the world ... is 1/N . Let the ith cell contain m i particles on completion. Then associate with this cell the probability a i = m i /m and withdraw the particles. 2. The other n particles...

Ngày tải lên: 07/08/2014, 07:21

... of the Gessel-Viennot method. The interpretation of ω as the number of Ceratic Hankel paths follows from the determinant using the Gessel-Viennot theorem (theorem 2). Furthermore, theorem 4, the ... C 0 = 1, in the expansion of κ(ω). To distinguish the steps of the original path from the steps of the inserted paths we will colour the former red and the latter blue....

Ngày tải lên: 07/08/2014, 08:20

... a i and black b i vertices on one side of , and the edges of all black a i and white b i vertices on the other side of .LetG + be the subgraph on one side of ,andG − the subgraph on the other ... 2, while the second creates a ({2,s− 1}; 1)-corner. To the former, apply the theorem for p = P − 1andk = 2, and apply the theorem for p =1andk = 1 to the latter. Both r...

Ngày tải lên: 07/08/2014, 08:22

... together nicely. In Section 3 we recall several useful results from [11], and then prove this theorem. Sections 4 and 5 are devoted to the applications of Theorem 3.1 to geometric lattices and ... together, these results (along with those of Chari and Swartz) give us the following. Theorem 1.1. Let ∆ be the order complex of a rank-selected subposet of either 1: a geometric latti...

Ngày tải lên: 08/08/2014, 12:23

... study the properties of the polynomials using the Poisson central moments, and we derive Relation (1.6) as a corollary. Finally in Section 4 we state the connection between these polynomials and the ... moments of the Poisson distri- bution. We show that these polynomials are dual of the Charlier polynomials by the Stirling transform, and we study the resulting combina...

Ngày tải lên: 08/08/2014, 14:22

... x 2 u ≥ 1 k x 2 w ≥ 1 nD , completing the proof. Hereafter, we assume that dist H (w, u) ≥ D and, by symmetry, dist H (w, v) ≥ D. Let P (u, w) and P (v, w) be shortest paths joining u and v to w in G. If u ∈ P (v, w) , then there ... 1, joining w to u in G, and thus in H, a contradiction. Hence, u /∈ P (v, w) and, by symmetry, v /∈ P (u, w) . Therefore, the paths P (u, w) and P...

Ngày tải lên: 07/08/2014, 13:21

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Ngày tải lên: 05/08/2014, 15:21