Báo cáo toán học: "Counting Bordered Partial Words by Critical Positions" ppt

... 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

... characteristic series is uniquely determined by the functional equation B =  +(u +¯u)BdB. (2) Let B n be the set of words in B that are of length 2n,andletB n,k be the set of words in B n with k occurrences ... letters. We define the reduction of v, denoted red(v), by red(v)(i)=|{j : v j ≤ v i }|. In other words, red(v) is the permutation of [n] obtained from v by replacing the sma...

Ngày tải lên: 07/08/2014, 13:21

... give rise to languages on A recognized by slight modifications of this automaton. For i ∈{0, 1, 2} and j ∈{0, 1, 2},wedenotebyL ij the set of words accepted by the basic automaton that start at ... nor factor DD. Such words just consist of a letter in B followed by a word avoiding factors CC and DD. As the set of words avoiding factors CC and DD is exactly recognized by the autom...

Ngày tải lên: 07/08/2014, 13:21

... counting k-ary words of length n as this paper does, consider counting k-ary words with weight m. For example, the ordinary generating function for k-ary words with occurrences of 1 p marked by u and ... number of words σ with k’s in the positions given by the subset. The quantity N m is given by N m =  p m  f r (n − m, k), since inserting m copies of k into any of the first p...

Ngày tải lên: 08/08/2014, 14:23

... primitive) words can be generated by some Marcus contex- tual gramma r. 2000 Mathematics Subject Classification: 68Q45. Keywords: Periodicity of words, primitive words, strongly primitive words, hyper ... of Hyper Primitive Words In this section, first we characterize a quasi-periodic word. Definition 5.1. Let u ∈ X + be a quasi-periodic word and let any letter in u be covered by a wo...

Ngày tải lên: 06/08/2014, 05:20

... result is best possible. In other words, if our lower bounds for the β j were actually equalities, then the lower bound given by (6) is sharp. We will accomplish this by showing that the M n (T), ... ξ-function is defined by ξ(s)=H(s)ζ(s), where H(s)= 1 2 s(s− 1)π − 1 2 s Γ( 1 2 s)and ζ(s)istheRiemannζ-function. The zeros of ξ(s) and its derivatives are all located in the critical str...

Ngày tải lên: 07/08/2014, 06:20

... 1973. (A revised edition, entitled The Encyclopedia of Integer Sequences,byN.J.A.Sloane and S. Plouffe, is to be published shortly by Academic Press.) 12. S. V. Tsaranov, On a generalization of Coxeter ... from the pentagon and hexagon graphs by this procedure. All this material can be found in Seidel [9]. Let (X, V ) be a two-graph. Define a relation ≡ on X by setting x ≡ y if either x =...

Ngày tải lên: 07/08/2014, 06:20

... are counted by the Schr¨oder numbers ([23], exercise 6.39.b) and it is easy to give a proof by GF; we omit the details. The extremal values of e(H)andi(H) follow from the formulas by substituting ... point is connected to (0, 0) by a lattice path that makes steps only (0, 1) and (1, 0) and lies completely in X and (ii) words over {−1, 0, 1} of length n −2 with nonnegative partial...

Ngày tải lên: 07/08/2014, 06:20

... combinatorics 7 (2000), #R40 9 where, for P ∈ A  2 (n), G(P ) is obtained by replacing each blue HV pair by D step and by removing the color from any red turns. Finally, with the maps h : A 0 5 (n) ... L 3 (n) where, for P ∈ L c 2 (n; 2), the path f(P ) is simply obtained by replacing each blue peak, i.e., blue VH pair, with the step D and by removing the color from each red peak....

Ngày tải lên: 07/08/2014, 06:20

... for n remains open. ∗ The research of the first author was partially supported by NSERC of Canada. † The research of the second author was partially supported by the Fund “Peregrinatio I” of MOL Co. Hungary, ... been obtained by B3.3, in which case the preimage is ({v 1 ,v 2 ,v 3 },a). If {v 1 ,v 2 ,v 3 } is coplanar with a (and therefore b/∈H i ), then the tuple can only have been obtai...

Ngày tải lên: 07/08/2014, 06:22