Báo cáo toán học: "Improved bounds for the number of forests and acyclic orientations in the square lattice" doc

... several counting problems on the square lattice L n . There the authors gave the following bounds for the asymp- totics of f(n), the number of forests of L n ,and (n), the number of acyclic orienta- tions ... y>0andz t y =1. the electronic journal of combinatorics 10 (2003), #R4 15 Improved bounds for the number of forests and acyclic...

Ngày tải lên: 07/08/2014, 07:21

... to ( 2). the electronic journal of combinatorics 17 (2010), #N24 3 For the identities displayed in (1) and (2) , their linear combinations yield the fo llowing respective symmetric forms n  k=0 a a ... the finite differences of a polynomial results in zero if the polynomial degree is less than the order of differences. 2 Proofs of the Abel Formulae According to th...

Ngày tải lên: 08/08/2014, 11:20

... either of these is the result of deleting the letters {3, 4, ,k− 4} from w,thenw must be either a word starting within the 0v 1,k−4 block and ending at the end of x k or a word starting at the ... in w 3 ,allofw 2 is contained in h k−1 ,sothereisapairof 2’s in w k−1 . The half-way point for s 3 , however, is in w 1 , so all four appearances of 2 are to the ri...

Ngày tải lên: 07/08/2014, 08:20

... ≥ 402 improving on the best previously known bounds k 3 (7) ≥ 153 and k 3 (8) ≥ 398. The proofs are founded on a recent technique of the author for dealing with systems of linear inequalities ... satisfied by the number of elements of C, that lie in k-dimensional subspaces of F n 3 . The method presented in [3] is limited by k ≈ n 2 . The reason is, that for...

Ngày tải lên: 07/08/2014, 15:22

... Main lemmas and proof of Theorem 1.1 In this section we give the overall structure of the proof of Theorem 1.1, including the required basic definitions and two key lemmas–whose validity imply the ... those times in which new edges are added to the evolving graph), Bohman expresses the expected change in the values of the random variables in the collection...

Ngày tải lên: 07/08/2014, 21:21

... pairs of edges. Then, we apply Relation 1 and Operations 1,2 and 3 to normalize the polygon P and get the genus of the embedding. Based on joint trees, the topo lo gical problem for determining ... with minimum degree at least three. A frame of G is obtained recursively by (1) for every vertex of degree four incident to a loop, deleting the loop and contracting o...

Ngày tải lên: 08/08/2014, 12:23

... below). For information about publishing your research in Journal of Inequalities and Applications go to http://www.journalofinequalitiesandapplications.com/authors/instructions/ For information ... provided the main idea in this article. S-WH carried out the proof of inequality (2.1) in this article. Z-HS carried out the proof of inequality (2.2) in this article. Al...

Ngày tải lên: 20/06/2014, 21:20

... g5toincreasebyoneonly(ifwetakei4andi6ascodewords). But then the covering of h2, f0andh0 requires an increase of the degree of g1ofat least two, and in the best case we end up with degrees four, three and four for e5,g5 and g1, respectively. ... take h3inC:nowg3isinL ≥3 ∩C and the degrees of g5 and g1 both increase. The covering of h6, f0andh0 will necessarily...

Ngày tải lên: 07/08/2014, 06:20

... each other triplet in the block, in such a way that a parity condition holds: the sum of the 20 labels is divisible by 3. The number of choices for each block is then 21 ×3 19 , and the total number ... pn elements of A.LetA  be the remaining (p − β(p))n elements of A. Consider the partition, P , of the elements of F into groups depending on the valu...

Ngày tải lên: 07/08/2014, 06:22

... coloring of the edges of K r,r contains either a red K m,m or a green K n,n . In early work on the subject [1], Beineke and Schwenk proved that b(2, 2) = 5 and b(3 , 3) = 17. In [4] Hattingh and ... n) is the smallest positive integer r such that every (red, green) coloring of the edges of K r,r contains either a red K m,m or a green K n,n . We obtain asymptotic bou...

Ngày tải lên: 07/08/2014, 06:22