Báo cáo toán học: "Improved bounds on the length of maximal abelian square-free word" pot

... particular, it contains exactly one occurrence of the greatest letter it contains, since between two the electronic journal of combinatorics 11 (2004), #R17 3 Improved bounds on the length of maximal abelian square-free ... m. Further, if there is a pair of (k − 1)’s in w m , one must be on the left half of s m and hence before the m in h m+1 ,and the other...

Ngày tải lên: 07/08/2014, 08:20

... 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 ,andα(n), the number of acyclic orienta- tions of L n :3.209912 ... acyclic orientation on the corresponding comb graph. A simple adaptation of the last proof also gives a proof of the following the electronic jour...

Ngày tải lên: 07/08/2014, 07:21

... Denote by SF n k, the number of (k, )-sum-free subsets of [1,n]. Since the set of 1 the electronic journal of combinatorics 7 (2000), #R30 7 Proof. We need to show that the left-hand side of (4) is ... completes the proof of Theorem 2. Corollary 1. The estimate (5) holds, provided k>≥ 3 and max  1+ln 2 2 (k − ), 2(1 + ln +1 2 )   +1 < ln 2 ρ . (9) the e...

Ngày tải lên: 07/08/2014, 06:20

Ngày tải lên: 05/08/2014, 15:21

... relation is derived for the rank (over most fields) of the set-inclusion matrices on a finite ground set. Given a finite set X of say v elements, let W = W t,k (v) be the (0,1)-matrix of inclusions for ... A note on the ranks of set-inclusion matrices D. de Caen Department of Mathematics and Statistics Queen’s University Kingston, Ontario, Canada K7L 3N6 decaen@mast.queensu...

Ngày tải lên: 07/08/2014, 06:22

... bipartite digraphs, namely, specifying conditions on the cardinality of the edge-set of the digraph that guarantee the existence of a directed simple cycle of length at most four. As usual in Tur´an ... ,2ρn.Denotethisblock M 2 .DenotebyM 3 the block consisting of the rows i = |A + |+1, ,m and the columns j =1, ,ρn.DenotebyM 4 the block consisting of the rows...

Ngày tải lên: 07/08/2014, 06:23

... not strong and that no sets A and B satisfy the lemma. Let t be the number of strong components of T − v and let W i be the set of vertices in the i th strong component. If |W 1 |≥3, then choose a ... u 1 u 2 ···u m−1 and apply the induction hypothesis using the paths P and Q  to obtain a path R  satisfying the lemma. Next, we repeat the above argument with the porti...

Ngày tải lên: 07/08/2014, 13:21

... ε d−1 by the choice of δ. This proves the claim. (3) The proof is similar to the proof of Claim 4.8 (2). (4) The proof is similar to the proof of Claim 4.8 (1).  the electronic journal of combinatorics ... Note that the above lower bounds trivially imply similar lower bounds on the expectation of e(M n (H)). It is worth mentioning that all of the above l...

Ngày tải lên: 07/08/2014, 21:21

... a non- empty Dyck prefix a nd k (resp. t) is the number of all consecutive falls in the end of τ (resp. p). Proof. Using the bijection of Fig. 6, under the inequality restrictions of relations ... λµλ is the greatest border of λµλµλ, for ν ≥ 3. Proposition 5. If w = (λµ) ν λ is the canonical form of the periodic word w, then v is a border of w iff it is either a bord...

Ngày tải lên: 08/08/2014, 14:23

... vertices, which is the main result of the paper. The o r ganization of the paper is as follows. In the rest of this section we introduce basic notations. In Section 2, we verify the conjecture for ... is the intersection graph of a set I = {I 1 , . . . , I n } of intervals (arcs) on a circle C, i.e. if there exists a one-to-one correspondence between the vertices...

Ngày tải lên: 08/08/2014, 14:23