Báo cáo toán học: " Combinatorial and Automated Proofs of Certain Identities" pdf

... completes the proof of Theorem 2. 4 Automated Proofs 4.1 Proof of Theorem 1 Since the summands on the left and right sides of equation (1) va nish outside the intervals [0, m] and [0, n], the ... generatingfunctionology and the the Wilf-Zeilberger (WZ) method. Enumerative combinatorics deals with counting the number of certain combinatorial objects. It gives meaning and...

Ngày tải lên: 08/08/2014, 14:23

... absorbers hav ing energy band gaps in the range of 1.3 to 1.5 eV compared with CdS and having a wider energy band gap compared with CdS, which trans- mits even higher energy photons and increases the ... National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0024830). Author details 1 School of Materials Science and Engine...

Ngày tải lên: 20/06/2014, 21:20

... study and participated in its design and coordination. CY participated in the revision of the manuscript. LPS and YW participated in the preparation of the TiO 2 /ZrO 2 bilayer thin film. JQZ and ... full incorporation of the TiO 2 and ZrO 2 film, as shown in TEM. Figure 2 High-resolution cross-sectional TEM images of the interface between the composite thin films and Si.(...

Ngày tải lên: 20/06/2014, 21:20

... Semigroups Yupaporn Kemprasit 1 and Sawian Jaidee 2 1 Department of Mathematics, Faculty of Science Chulalongkorn University, Bangkok 10330, Thailand 2 Department of Mathematics, Faculty of Science , Khon ... set of integers and the set of real numbers, respectively. In [3], Kemprasit and Changphas characterized when OT (X) is regular where X is a nonempty subset of Z or X...

Ngày tải lên: 06/08/2014, 05:20

... those of the author(s) and do not necessarily reflect the views of the NSA. the electronic journal of combinatorics 11 (2004), #R4 1 2 The Proofs Let n(G) denote the number of vertices of a graph ... N(z) since d(x) ≥ d(z), and the 2-switch that replaces wz and xy with wx and zy reduces the number of missing desired neighbors of w. Theorem 4 For a positive list X and...

Ngày tải lên: 07/08/2014, 08:20

... G 1 and G 2 in the embedding of G. G 1 is completely embedded in one of the faces of G 2 and vice versa, which is not possible by convexity of faces and by Lemma 15. If G O has a vertex of degree ... vertex of degree two and either connected or two-connected. By Lemma 13 and Lemma 14 there is a subset of vertices V 1 and a component G 1 of G O \V 1 such that G 1 ∪V...

Ngày tải lên: 07/08/2014, 13:21

... vertex z 0 of K 4 is precoloured, each edge incident with z 0 is given a list of three colours not including the colour of z 0 , and every other vertex and edge of K 4 is given a list of five colours, ...  ∆ + 1, and suppose that every vertex and edge of G is given a list of ∆ + 1 colours. Then the vertices and edges of G − (B − z 0 ) can be properly coloured from th...

Ngày tải lên: 07/08/2014, 13:21

... set and the vertex set of G is denoted by V (G) and E(G) respectively. For a vertex v of G, the degree, d(v), of v in G is the number of edges incident with v. The set N v of all neighbours of ... finish the proof of the theorem. Case 2.1: α ∈ ¯ϕ(y) ∪ ¯ϕ(z). By the symmetry between y and z, we can suppose that α ∈ ¯ϕ(y). By (a) and (b), there is a colour β ∈ ¯ϕ(x) and a...

Ngày tải lên: 07/08/2014, 15:22

... limit distribu- tions of the number of edges in a random dissection and in a random outerplanar graph, respectively. Proof of Theorem 1.4. The limit distribution of the number of edges in a two-connected unlabeled ... probability of connectedness, the number and type of components, and the number of isolated vertices, in a random outerplanar graph. Next, we investigate t...

Ngày tải lên: 07/08/2014, 15:23

... aba and bab in our comma-free dictionary, so for each pair of letters, there is either a counted word of the form abb or bba or of aab or baa. Without loss of generality, assume we have abb and ... size of each word is k and the size o f the alphabet is n, the maximum numb er of elements in D is denoted as W (k, n). Golomb, Gordon, and Welch [4] established a bound for the...

Ngày tải lên: 07/08/2014, 21:21