Báo cáo toán học: "The many formulae for the number of Latin rectangles" doc

... (2004) doi:10.1186/1687-1812-2011-106 Cite this article as: Zhu et al.: Weak convergence theorem for the three-step iterations of non-Lipschitzian nonself mappings in Banach spaces. Fixed Point Theory and Applications 2011 2011:106. Submit ... Shahzad, N: Convergence theorems for a common fixed point of finite family of nonself nonexpansive mappings. Fixed...

Ngày tải lên: 20/06/2014, 21:20

... δ). We establish these values in Sections 2, 3 and 4. TIGHT UPPER BOUNDS FOR THE DOMINATION NUMBERS OF GRAPHS WITH GIVEN ORDER AND MINIMUM DEGREE W. Edwin Clark University of South Florida Tampa, ... y.IfA⊆V then we let A denote the subgraph of G induced by A. Table 1 contains the value of γ(n, δ) for n ≤ 16, 0 ≤ δ ≤ n − 1 if the value is known, ot...

Ngày tải lên: 07/08/2014, 06:20

... referee for numerous comments and suggestions which have led to a substantially improved paper. An Asymptotic Expansion for the Number of Permutations with a Certain Number of Inversions Lane Clark Department ... Eds., Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, Dover Publications, New York, 1966. [2] E .A. Bender, Central...

Ngày tải lên: 07/08/2014, 06:20

... graph of order n with domination number at least 3 and minimum degree δ satisfying n −2 √ n −4 ≤ δ ≤ n − √ 2 √ n. Tight Upper Bounds for the Domination Numbers of Graphs with Given Order and Minimum ... combinatorics 7 (2000), #R58 19 [2] W. Edwin Clark and Larry A. Dunning, Tight Upper Bounds for the Domination Numbers of Graphs with...

Ngày tải lên: 07/08/2014, 06:22

... v(G) denote the number of vertices, and (G) denote the number of edges. In this paper, we construct a graph G having no two cycles with the same length which leads to the following result. Theorem. ... Chunhui Lai, On the size of graphs with all cycle having distinct length, Discrete Math. 122(1993) 363-364. [6] Chunhui Lai, The edges in a graph...

Ngày tải lên: 07/08/2014, 06:22

... combinatorics 10 (2003), #R35 14 Bicoloured Dyck paths and the contact polynomial for n non-intersecting paths in a half-plane lattice. R. Brak† and J. W. Essam‡ ∗ †Department of Mathematics, The ... configurations of a single path starting at vertex v i α and ending at vertex v f β . The theorem may be used to find the Hankel n path contact polynomial...

Ngày tải lên: 07/08/2014, 08:20

... invalid in the other.) This lemma, together with the discussion preceding it, completes the proof of formula (18). We leave to the reader the task of showing that this formula reduces to formula (4) ... t). In other words, the statistics for labelled paths inside the triangle with vertices (0, 0), (0,n), and (mn, n) give a combinatorial interpretation for the Hilber...

Ngày tải lên: 07/08/2014, 08:20

... set. Vertices of R G ì D H are the electronic journal of combinatorics 12 (2005), #N12 4 Vizing-like conjecture for the upper domination of Cartesian products of graphs – the proof Boˇstjan Breˇsar ∗ University ... prove the following conjecture of Nowakowski and Rall: For arbitrary graphs G and H the upper domination number of the Carte...

Ngày tải lên: 07/08/2014, 08:22

... is the number of times the integer i occurs in the sequence T . Note that the sum of all b(i), 1 ≤ i ≤ n,isequaltol, the length of T . 3 A simple proof for the existence of exponentially balanced ... two, or are two successive powers of two. A proof for the existence of exponentially balanced Gray codes is derived. The proof is much sim- p...

Ngày tải lên: 07/08/2014, 08:22

... b) -partition for every pair (a, b) of positive integers such that a + b = τ(G), then we say that G is τ-partitionable. The following conjecture is known as the Path Partition Conjecture (or the ... section we state our two main theorems, together with the main lemmas and the partition strategy used in the proofs. The proofs are presented in Section 4. The Partition...

Ngày tải lên: 07/08/2014, 13:21

... related to the automorphism groups of trees have been investigated. We state, for instance, the enumeration of identity trees (see [7]), and the question of determining the average size of the automorphism ... to G. Labelle for the summed cycle indices of all rooted trees, which resembles the well-known formula for the cycle index of the symme...

Ngày tải lên: 07/08/2014, 13:21

... agree above row r and to the left of column c (and the definitions of r and c) we see that the only possibility for /à is (r, c), completing the proof of this case and the theorem. Acknowledgements. ... 308, 9 (2008), 1524–1530. the electronic journal of combinatorics 15 (2008), #N23 4 A sharp bound for the reconstruction of partitions Vincent Vatter Departme...

Ngày tải lên: 07/08/2014, 15:22

... Robinson-Schensted correspondence for the signed Brauer algebra using bidomino tableau 4.1 The Knuth relations In this section, we derive the Knuth relations for the signed Brauer algebra by using the Robinson-Schensted ... give the method for translating the vacillating tableau to the bi-domino tableau. We also give the Knuth relations and the determin...

Ngày tải lên: 07/08/2014, 15:22

... interpretation of the closed formula (10) for the number of con- vex permutominoes. We remark that the expression of f n resembles the expression (1) for the number c n of convex polyominoes of semi-perimeter ... : the uppermost cell of the rightmost column of the polyomino has the maximal ordinate among all the cells of the polyomino; U2 :...

Ngày tải lên: 07/08/2014, 15:22

... Beissinger, who was the first to explore [1] combinatorial proofs using colored permutations, for their assistance. References [1] Janet Beissinger. Colorful proofs of generating function identities. ... follows for (π, f ) ∈ S n,A : If R (π,f) = ∅, let φ((π, f)) = (π, f). Otherwise, let (i, j) ∈ R (π,f) be minimal under the lexicographic ordering of R (π,f) . Let ˜π = (i, j)...

Ngày tải lên: 08/08/2014, 01:20