Báo cáo toán học: "Bordered Conjugates of Words over Large Alphabets" pot

... 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 of Words over Large ... 1. This concludes the proof. We now show that almost all binary words of length n are β-images. Proof of the main Theorem 1. Let u ∈ {a, b} ∗ be a nonempty binary word of...

Ngày tải lên: 07/08/2014, 15:22

... x u m u y u As e is a suffix of u, we have: p u = p e , y u = y e , and µ(x e )µ(m e ) is a suffix of µ(x u )µ(m u ), thus x e m e is a suffix of x u m u . Moreover, e is a prefix of u, so s u = s e , x e = ... α + -free) if none of its subwords has exponent β, with β ≥ α (resp. β > α). The critical exponent of an infinite word w over A is defined as E c (w) = sup {E(v) ∈ Q, v subword...

Ngày tải lên: 08/08/2014, 14:23

... Kayoko Shikishima-Tsuji 3. Set of Primitive Words In this section, we deal with the set of all primitive words. First we provide the following three lemmas . The proofs of the lemmas are based on ... L in (G). Thus the statement of theorem m ust hold true.  By the above proof argument, we have the following. Corollary 5.1. The language HQ of all hyper primitive words over an...

Ngày tải lên: 06/08/2014, 05:20

... other words, the white corners are the southeast corners of the components of the diagram. The essential set E(w)ofapermutationw is defined to be the set of white corners of the diagram of w. For ... set of distributions of n −2 chips. This completes the proof of Theorem 2.1. ✷ 3 Enumerative aspects of the essential set The combinatorial object that we are studying is the es...

Ngày tải lên: 07/08/2014, 06:20

... formed by reversing the order of the rows of M. As for the matrix P of 3.1.3(2), we have seen above that it is the integral encoding of the rectification S of any tableau T of which M is the integral ... of its rows, and Q is the integral encoding of the Q-symbol under the RSK correspondence of the matrix obtained from M by reversing the order of its columns. Note that reve...

Ngày tải lên: 07/08/2014, 13:21

... te of eq uivalence of length < 2 n 2 /2 . Proof By Proposition (1) the chromatic polynomials of G and G ′ can each be expressed as a sum of complete graphs in at most 2 m − 1 applications of ... list the numbers of chromatic polynomials of degree at most 9 with certificates that use sequences of steps of the kind we have been discussing, with p ≥ 0. Examples of certificat...

Ngày tải lên: 07/08/2014, 21:21

... copy of H] → 1 as n → ∞. Sketch of Proof We work with the set of graphs that don’t have any copies of H. By Lemma 4, we may assume that we have lots of pendant edges, so we may delete |H| of these ... decent proportion of graphs with lots of isolated vertices, but no components isomorphic to C. If such a graph contains lots of copies of C, then we may ‘transfer’ the edges...

Ngày tải lên: 08/08/2014, 11:20

... elements of [n] × [n]. Clearly, the union of all such Q ′ i s is a subdiagonal quasi-permutation of cardinality n − k. An example of the map ϕ is given in Figure 3. the electronic journal of combinatorics ... are multiples of the central factorial numbers of odd indices a nd we also establish a simple derivation of the explicit formula of Jacobi-Stirling numbers. 2 Jacobi-St...

Ngày tải lên: 08/08/2014, 12:22

... 121a 92 + 1837, the electronic journal of combinatorics 13 (2006), #R43 13 number of words of weight i in C and B j the number of words of weight j in the dual C ⊥ of C (if the code needs specifying, ... of several four-dimensional codes over GF(8) that meet the Griesmer bound. The proofs use geometric methods based on the analysis of the weight structure of subcodes....

Ngày tải lên: 07/08/2014, 13:21

... self-avoiding words over a finite alphabet. Fur- thermore, he shows that for each k there exists a longest finite self-avoiding word x over an alphabet of size k. Call n(k) the length of such a word. ... the end of the queue. the electronic journal of combinatorics 8 (2001), #N2 2 Weakly Self-Avoiding Words and a Construction of Friedman Jeffrey Shallit ∗ and Ming-wei Wang Depa...

Ngày tải lên: 07/08/2014, 06:22