Báo cáo toán học: " Tiling Parity Results and the Holey Square Solution" ppt

... paper answers the holey square conjecture in the affirmative via a theorem about tiling parity with applications beyond the problem of the holey square. We demonstrate some of these other consequences. As ... of the proof follows analogously to the case p =1. 3 The holey square As discussed in the introduction, the resolution of the holey square conjecture...

Ngày tải lên: 07/08/2014, 08:22

... 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

... 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 l...

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

... further functions: F 2, which consists of the composition of (18vi) and F3; and FO, which consists of the composition of F 2, FI, and (181) and defines the overall function effected by the ... (18)(ii) and (iv) generate values of z' independently from values of x and y, and these are then taken by (18)(ill) and (v), respectively, to generate values of z, th...

Ngày tải lên: 18/03/2014, 02:20

... − 2 3  2π 2 − 46 3  . The fourth derivative of the HC on the argument n, and the common radius is of the form Figure 8 The HC and its derivative with the HC maximum location and optimum for the value of the degree ... [17], and others and for its testing, see Letić et al. [18]. Today the results of the HC researc h are represented both in geo- metry and t...

Ngày tải lên: 20/06/2014, 21:20