Báo cáo toán học: "Critical exponents of words over 3 letters" pps

... example, δ(0110) = 110. Lemma 1. Let L be the set F act(µ(A ∗ 3 )) of all subwords of the words in µ (A ∗ 3 ). Let α ∈]7/4, 2[ and v ∈ A ∗ 3 , such that: - abcbabcv ∈ L - abcbabcv is α-free. Suppose ... µ. Proposition 2. Let w be a word over A 3 , and u a subword of µ(w). If |u| ≥ 1 8 , then, there exists a unique x ∈ A 3 , a unique y ∈ A 3 , and there exist some unique...

Ngày tải lên: 08/08/2014, 14:23

... A, 30 (2):1 83 2 03, 1981. [4] T. Harju and D. Nowotka. Border correlation of binary words. J. Combin. Theory Ser. A, 108(2) :33 1 34 1, 2004. [5] M. Lothaire. Combinatorics on Words, volume 17 of ... A ∗ of length k a by Theorem 2, and Lemma 3 shows how to construct a word w  such that β(w  ) = u. the electronic journal of combinatorics 15 (2008), #N41 5 Bordered Conjugates o...

Ngày tải lên: 07/08/2014, 15:22

... Fig. 1 .3 indicates that u is a quasi-periodic word. Fig. 1 .3. Vietnam Journal of Mathematics 34 :4 (2006) 38 1 38 7 Some Periodicity of Words and Marcus Contextual Grammars * P´al D¨om¨osi 1 ,G´eza ... denotes the set of all suffixes of w.Ifu is not quasi-periodic, then it is said to be hyper primitive. By HQ we denote the set of all hyper primitive words. Remark 1 .3. Fig....

Ngày tải lên: 06/08/2014, 05:20

... first over all cycles, H 1 , of length r 1 , and then over all intersecting cycles H 2 of length r 2 . Noting that H 2 − E(H 1 ) is a collection of a paths for some a ≥ 1, we sum over the number of ... expected number of t-tuples of non-edge-disjoint cycles of lengths r 1 , ,r t is o(1) for any t ≥ 2, and so for any x 1 , ,x s , the electronic journal of combinatorics 6 (...

Ngày tải lên: 07/08/2014, 06:20

... x0 y0 w3 h1" alt=""

Ngày tải lên: 05/08/2014, 15:20

... result. the electronic journal of combinatorics 8 (2001), #R30 5 We now restate Theorem 2.2 in terms of the coefficients of P . Theorem 2 .3 Let 0 ≤ a 0 ≤ a 1 ···≤a m be a sequence of real numbers and n ... that d j = m  k=j a k  k j  (2) and a j = m  k=j (−1) k−j d k  k j  . (3) Lemma 3. 1 Let 0 ≤ j ≤ m. Then a j ≥ 0 ⇐⇒ d j ≥ m  k=j+1 (−1) k−j+1 d k  k j  . (4) Proof This f...

Ngày tải lên: 07/08/2014, 06:22

... edge-disjoint union of two paths of length n,wheren ≥ 2. Using a result of Thomason on decompositions of 4-regular graphs into pairs of Hamiltonian cycles, we prove that G hasathirdpathoflengthn. the ... path of length n. For example, the complete graph K 4 is an edge-disjoint union of two paths of length 3, each path meeting the other in four vertices. The cycle C 6 is the e...

Ngày tải lên: 07/08/2014, 06:23

... factorizations to the set of type B parking functions. For example the label of the factorization (−1 − 2 − 31 23) =[(12)(−1 − 2)] [ (3 − 3) ] [(−2 3) (2 − 3) ] is 133 . There is again an action of S n on factorizations, ... the set of all such factorizations to the set of parking functions. The above considerations show that this is just a rephrasing of Stanley’s Theorem 3....

Ngày tải lên: 07/08/2014, 06:23

... ordering of the vertices to an ordering of the edges lexicographically. A broken circuit of H ⊆ G is a set of edges B ⊆ H such that there is some edge e ∈ G, smaller than every edge of B, such ... evaluates to the number of proper colorings of G with x colors. The subgraph expansion of χ G (x)is χ G (x)=  Q⊆G (−1) |Q| x c(Q) where c(Q) is the number of components of Q. Se...

Ngày tải lên: 07/08/2014, 08:22

... Ser A 43 (1986), 1 03 1 13; Erratum 44 (1987), 31 0. [15] J.R. Stembridge, Some hidden relations involving the ten symmetry classes of plane partitions, J. Combin. Theory Ser. A 68 (1994), 37 2–409. [16] ... remaining cases of the weighted enumeration of self–complementary plane partitions contained in a given box where adding one half of an orbit of cubes and removing the other...

Ngày tải lên: 07/08/2014, 08:22