Báo cáo toán học: "New Upper Bounds for the Size of Permutation Codes via Linear Programmin" pdf

... new bounds for µ(n, d) for small values of the param- eters n and d. In [15], H. Tarnanen uses the conjugacy scheme of the group S n in order to obtain new upper bounds fo r the size of a permutation ... obtain sharper upper bounds, other linear constraints on the coefficents a i must be considered. The following theorem motivates the study of permutati...

Ngày tải lên: 08/08/2014, 12:22

... provide upper bounds on the orders of (k, g)-cages. Namely, Theorem 2.1 [7] Let G be a k-regular graph of girth at least g having the least number of vertices. Then the girth of G is g and the diameter ... by F¨uredi, Seress and the authors, see [9]. The fact that the orders of these constructions actually meet the upper bound in (2) for q odd follows from [1...

Ngày tải lên: 07/08/2014, 06:22

... contains the value of γ(n, δ) for n ≤ 16, 0 ≤ δ ≤ n − 1 if the value is known, otherwise upper and lower bounds for γ(n, δ). We establish these values in Sections 2, 3 and 4. TIGHT UPPER BOUNDS FOR THE ... either two A v ’s of the form {x, z} and {y,w} or, of the form {x, w} and {y, z}. But this contradicts our assumption that the two element A v ’s are never d...

Ngày tải lên: 07/08/2014, 06:20

... definition of δ k (n). The theorem therefore follows. In the next section we show that if k = 3 then the above theorem holds for n ≥ 6. Note that the results in this section are stated for fixed ... The theorem therefore follows from the definition of δ k+1 (n) which is the maximum value of δ for which γ(n, δ) ≥ k +1. We shall show that this upper bound is quite tight...

Ngày tải lên: 07/08/2014, 06:22

... automorphism of Γ p . (4) The graph Γ p was defined for the first time in [8]. In [8] it is also proved that Γ p → (3,p) for p ≥ 3. For the proof of the main theorem we shall also use the following ... have cl(G i )=a i − 1 for i =1, 2. (14) From (13), (14) and Lemma 1 we conclude that The number of the vertices of each connected component of ¯ G 1 is an even num...

Ngày tải lên: 07/08/2014, 13:21

... (14) is the best in all known upper bounds for G 2 , and bound (18) is the best in all known upper bounds for G 3 . Finally, bound (22) is the best upper bound for G 1 and bound (1 8) is the second-best ... r i =  j=i |a ij | for each i = 1, 2 , . . . , n, then Lemma 2.2. [15] Let A = (a ij ) be a complex matrix of order n  2. Then the eigenvalues of the m...

Ngày tải lên: 08/08/2014, 12:23

... K k J in the upper left submatrix of T r+3 (of size 3(M − 1) × 3(M − 1)), then there must be a J-colored K k J in T r+2 (0, 2, 3, 4, ,r + 3), contradicting the definition of T r+2 . Remark: Up to the ... exactly the same places as in the upper left block, A. We further note that if (s, t)and(u, v) are two of the entries in question, then (s, t) ≡ (u, v)(mod M −1) (co...

Ngày tải lên: 07/08/2014, 06:20

... approximations of the roots for specific values of d are found easily, and so are the inverses of the roots of smallest modulus giving us the entries of first line of table 2. the electronic journal of combinatorics ... eight. However, the determination of the asymptotic behavior of the number of walks of finite memory is much easier. We can use the auto...

Ngày tải lên: 07/08/2014, 06:20

... stationary points of f, see [5] for more details. The fulfilment of this condition together with the context of the situation serves to characterise the local maxima of f. As an illustration of the local ... with area log n/n 2 for every fixed n; lower bounds on higher dimensional versions of the problem, produced in 1999 by G. Barequet [2] and the study of th...

Ngày tải lên: 07/08/2014, 06:23

... spoke. As the set of spokes form an edge-cut of the graph W (n, 2k +3), such a cycle must in fact use an even number of spokes. If the number of spokes used is four or more then the number of vertices ... number of vertices from the hub. the electronic journal of combinatorics 13 (2006), #R29 4 Constructive Upper Bounds for Cycle-Saturated Graphs of Minimum...

Ngày tải lên: 07/08/2014, 13:21