Báo cáo toán học: "Distinguishing Number of Countable Homogeneous Relational Structures" pptx

... distinguishing number two. the electronic journal of combinatorics 17 (2010), #R20 6 Distinguishing Number of Countable Homogeneous Relational Structures C. Laflamme ∗ University of Calgary Department of ... skeleton of a structure A is the set of finite induced substructures of A and the age of A consists of all relational structures isomorphic to an element of...

Ngày tải lên: 08/08/2014, 11:20

... The Number of Solutions of X 2 =0in Triangular Matrices Over GF(q) Shalosh B. EKHAD 1 and Doron ZEILBERGER 1 Abstract: We prove an explicit formula for the number of n × n upper triangular ... This formula was recently conjectured by Sasha Kirillov and Anna Melnikov [KM]. Theorem. The number of n × n upper-triangular matrices over GF(q) (the finite field with q elements), whose sq...

Ngày tải lên: 07/08/2014, 06:20

... sufficiently small, B is sufficiently near 1. ProofofTheorem3: Let a(G) be the number of automorphisms of an unlabeled n-vertex graph G. The number of distinct labelings of G is n!/a(G). If f (·)isa statistic ... This finishes the proofofTheorem1. 1.9 1.92 1.94 1.96 1.98 2 2.02 2.04 0 0.2 0.4 0.6 0.8 1 t Figure 2: The plot of µ  (t) for 0 ≤ t ≤ 1. 4 Proof of Theorems 2 and 3 Proof...

Ngày tải lên: 07/08/2014, 07:21

... provide the number of monic permutation binomials of a given degree m less than q − 1overF q , in terms of N 1 , N 2 and N 3,m ,whereN 3,m is the number of permutation binomials of the form x n (x 2 i s + ... count the number of permutation binomials for the other types. For the first one, since m − p ≡ 4 (mod 4), the number of such permutation binomials is N 2 .Thenumber...

Ngày tải lên: 07/08/2014, 13:21

... present an algebraic proof of a result with the same flavour as the latter: T n+2 (1, −1) = T n (2, −1), where T n (1, −1) has the combinatorial interpretation of being the number of 0–1–2 increasing ... to j in A. Let invA be the number of inversions in A. The inversion enumerator J n (y) is then defined as the generating function of spanning trees arranged by number of inver...

Ngày tải lên: 07/08/2014, 15:22

...  5 Remarks For the sake of completeness, we give references to the number of such basketball games for various values of w. For w = 2, ··· , 6 and w = ∞, the sequence of games ending at n : n ... T n−2 (z). (7) As an aside, note that if w = 2, the number of walks ending at (n, 0) give rise to the Fibonacci numbers and if w = ∞, the Catalan numbers [St]. 3 The Main Result - Bask...

Ngày tải lên: 07/08/2014, 15:22

... class of maximal K 3,3 -minor-free graphs and we can use the number of planar graphs and the number of triangulations as lower bounds. Determining the number (of graphs of sub-classes) of planar graphs ... asymptotic estimates for the number of planar graphs. Already in 1962, the asymptotic number of triangulations was given by Tutte [15]. Investigating how much the...

Ngày tải lên: 07/08/2014, 21:20

... set of q edges with weight at least s in a graph G. If the total weight of edges in Q is at most cq, then rep(L(G)) ≥ max k>s 2(k−c) (k−s)(k−s+1) q. Proof. Let X i be the number of edges of ... define the repetition number of a graph G, written rep(G), to be the maximum multiplicity in the list of vertex degrees. We study the minimum of rep(G) on various classes of n-ver...

Ngày tải lên: 07/08/2014, 21:21

... “intersection graph” of the components in G 1 and G 2 ). By construction, H is bipartite. The degree of a vertex in H is the number of vertices in the corresponding component of G 1 or G 2 . Each edge of H corresponds ... {a ∈ A: a /∈ B}. 2 Independence ratio at least 1/4 The independence number of a graph is the sum of the independence numbers of its components. Therefore...

Ngày tải lên: 07/08/2014, 21:21

... b in [St]). The number of planar trees with n + 1 nodes and the number of planar binary trees with n + 1 leaves are both given by the n’th Catalan number. It follows that the number of elements in ... journal of combinatorics 16 (2009), #R49 17 The crossing number e(M ǫ a,b , N ǫ ′ c,d ) is the minimal number of intersection of represen- tations of M ǫ a,b and N ǫ ′ c...

Ngày tải lên: 07/08/2014, 21:21