Báo cáo toán học: "Packing patterns into words" pptx

... quasi-periodic word and let any letter in u be covered by a word v. Then we denote u = v ⊗ v ⊗···⊗v. Some Periodicity of Words and Marcus Contextual Grammars 387 However, the other types of Marcus contextual ... set of all hyper primitive words. Remark 1.3. Fig. 1.3 indicates that u is a quasi-periodic word. Fig. 1.3. Vietnam Journal of Mathematics 34:4 (2006) 38...

Ngày tải lên: 06/08/2014, 05:20

... of repeating patterns of dense (and presumably optimal) packings of n equal non-overlapping disks in- side an equilateral triangle (see Fig. 1.1 for and example). It is natural to investigate ... RepeatedPatternsofDensePackings of Equal Disks in a Square R. L. Graham, rlg@research.att.com B. D. Lubachevsky, bdl@research.att.com AT&T Bell Laboratories Murray Hill...

Ngày tải lên: 07/08/2014, 06:20

... solves, in particular, the related problem in Coding Theory mentioned in the introduction. the electronic journal of combinatorics 4 (1997), #R1 2 is isomorphic to H. The H -packing number of G, ... divisor of the degrees of H. Clearly, if the conditions in Wilson’s Theorem hold, then the packing and covering numbers are known. In this paper we solve all of the conjectur...

Ngày tải lên: 07/08/2014, 06:20

... B´ona, Permutations with one or two 132-subsequences. Discrete Math. 181 (1998), no. 1-3, 267–274. [2] Aaron Robertson, Permutations containing and avoiding 123 and 132 patterns. Discrete Math. and ... π 1 is a permutation of the set {n − k +1, ,n−1} ,and 2 is a permutation of the set {1, ,n−k}. Furthermore, π 1 and π 2 are each (132)-avoiding. Conversely, if π 1 and π 2 are...

Ngày tải lên: 07/08/2014, 06:20

... a Construction of Friedman Jeffrey Shallit ∗ and Ming-wei Wang Department of Computer Science University of Waterloo Waterloo, Ontario, Canada N2L 3G1 shallit@graceland.uwaterloo.ca m2wang@math.uwaterloo.ca Submitted: ... non-weakly -self-avoiding words that are minimal in the sense that any proper prefix is weakly self-avoiding. Now we use a classical breadth-first tree trave...

Ngày tải lên: 07/08/2014, 06:22

... 3 Generalized patterns Here we consider packing generalized patterns into words. Generalized patterns were introduced by Babson and Steingr´ımsson [2] ... occurrences of patterns in Π (Π -patterns, for short) in a string σ. the electronic journal of combinatorics 9(2) (2003), #R20 4 with monotone and layered patterns in Section 2, with generalized patterns ... from permutations...

Ngày tải lên: 07/08/2014, 07:21

... electronic journal of combinatorics 10 (2003), #R8 9 Packing 10 or 11 Unit Squares in a Square Walter Stromquist Department of Mathematics Bryn Mawr College, Bryn Mawr, Pennsylvania, USA walters@chesco.com Submitted: ... ——, “Packing unit squares inside squares, II (ten unit squares) ,” DHWA Memo- randum, October 15, 1984. 6. ——, “Packing unit squares inside squa...

Ngày tải lên: 07/08/2014, 07:21

... interchangeably. Let P be an additive induced-hereditary property. Then P is reducible if it is the product of two additive induced-hereditary properties; otherwise it is irreducible.Itis true, though by ... graph in F(P) is connected. Every hereditary property is induced-hereditary, and the product of additive (induced-hereditary) properties is additive (induced-h...

Ngày tải lên: 07/08/2014, 08:20

... symbol of σ.Sincen +1>m, we can select a random subsequence of σ of length m by first throwing out one of the n + 1 symbols of σ at random and then randomly selecting a subsequence of length ... the following theorem of Stromquist. We give a proof which is somewhat shorter than the proof in [1], both for its own interest and because we will reuse the method of proof when stu...

Ngày tải lên: 07/08/2014, 08:22

... overlap. The problem of packing unit squares into a square was initiated by Erd˝os and Graham [2]. They prove that, for a large number s, unit squares can be packed into an s ì s square so that ... Lemma 5. Assume further that S does not contain point (min{2 ,a 1}, 0.9); a ≥ 3 is assumed (the case of a& lt;3 can be treated analogously). To estimate the minimum σ(S)inthiscase, w...

Ngày tải lên: 07/08/2014, 13:21

... 3: a unit equilateral triangle covered by 3 smaller equilateral triangles Proposition 3.4. T 1 (5) < 9 4 . Proof. Consider a covering of a unit equilateral triangle T with one equilateral triangle ... they have great practical and theoretical significance. In this paper, we discuss a problem on packing and covering a unit equilateral triangle w...

Ngày tải lên: 07/08/2014, 13:21

... 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

... y-ordinate from the bottom edge of Q k+1 to the top edge of Q k . For Q in Diagr am 3, δ(Q) =  2 3 6 4 4 5 3 2 3 5 5 2 6 5 4 1  . The map δ is a bijection from CCP to Y. As such, δ allows CCPs to be ... to a bipartition of N 2 . In this section, we use their Pattern Algebra to obtain a q-analog of Kitaev’s [25] Theorem 30 and to deduce a better generating function for per...

Ngày tải lên: 08/08/2014, 12:22

... example, δ(0110) = 110. Lemma 1. Let L be the set F act(à(A 3 )) of all subwords of the words in à (A 3 ). Let α ∈]7/4, 2[ and v ∈ A ∗ 3 , such that: - abcbabcv ∈ L - abcbabcv is α-free. Suppose ... à. 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 s,...

Ngày tải lên: 08/08/2014, 14:23

... nonsimple critical positions. Keywords: Theory of formal languages; Combinatorics on words; Number The- ory; Partial words; Bordered partial words; Simple border; Simply bordered partial words; Critical ... v is unbordered and is generated by a partial word u, then u is unbordered as well. Hence, every unbordered word over a k-letter alphabet with h holes c an be generat...

Ngày tải lên: 08/08/2014, 14:23