Báo cáo toán học: "Reconstructing permutations from cycle minors" pptx

... n-cycles or neither is an n -cycle. We consider these two cases separately. Case 1. Suppose neither p nor q is an n -cycle. Let k be the length of the cycle in p (and hence the length of the cycle ... permutation p “contains” the k -cycle (a 1 a 2 . . . a k ), or the k -cycle is “in” p, if it appears in the decomposition of p into disjoint cycles. 2 Reconstruction from Cycle Minors...

Ngày tải lên: 07/08/2014, 21:21

... a vertex of V 0 at distance in B at least m + 1 from the current set X 0 ,letu ∈ V 0 be one of such vertices chosen such that its distance in B from X 0 is minimum possible. Observe that dist G (u, ... path in B from X 0 (so u 0 ∈ X 0 )tou = u r ∈ V 0 .Then dist B (u i ,X 0 )=i for i =0, ,r. Suppose that r>2m. The vertices u m+1 , ,u r−1 do not belong to V 0 since their distance fro...

Ngày tải lên: 07/08/2014, 07:21

... N, the length of the tth row of this diagram (counting the rows from the bottom) is then N t =#{n: r A,B (n) ≥ t}. Wenoticethat from a well-known result of Pollard [P75] it follows that N 1 + ... ν k ≤ i + j −1 ≤ l + m − ν k } = lm − 2#{(i, j): i + j ≤ ν k } = lm − ν k (ν k − 1) and (4) follows from lm = ν 1 + ···+ ν k + ν k+1 + ···. Problem 3 What are the general properties shared by t...

Ngày tải lên: 07/08/2014, 08:22

... Incidentally, Entringer [13] enumerated “circula r ” permutations by peaks. the electronic journal of combinatorics 17 (2010), #R62 3 5.4 Permutations and up-down permutations by (i,m)-maxima For i  2 and ... generating function for permutations by a given pattern is deducible from the generating function for a related pattern permutation set; for instance, the generating function...

Ngày tải lên: 08/08/2014, 12:22

Ngày tải lên: 05/08/2014, 15:20

... reconstructible from its 3-deck. Proof. Similar to the proof of Theorem 7, with modifications as indicated in the proof of Theorem 6. Theorem 9 Let A ⊂  be locally finite. Then A is reconstructible from ... -linear combination of a finite set of elements from I. We will show that for finite subsets J with I 0 ⊂ J ⊂ I,thesetsA ∩J and B ∩J are equal, from which it easily follows that A...

Ngày tải lên: 07/08/2014, 06:20

... the case of permutations containing exactly one 132 pattern and r 12 k patterns. Introducing the modified total weight Ω k (q 1 , ,q k ) as the sum of the weights w k (π) over all permutations ...  Remark. For k = 1 one recovers from Theorem 2.1 the well-known generating function for the Catalan numbers, (1 − √ 1 − 4z)/2z. This result also follows im- mediately from Proposition 2.1 an...

Ngày tải lên: 07/08/2014, 06:20

... < 1/2) (50) and find from (41) G(x)= 2x 1 −2x − 1 2 + ∞  m=0 (−1) m 2  2m m  x 2m (1 −2x) = 1 2 1 −2x √ 1+4x 2 − 1 2 1 − 6x 1 − 2x . (51) On the other hand we have from (49) G(x)= x 1 − x + ... that the bond is directed from the first to the second index. If d =(i, j) we use the notation ˆ d =(j, i). Let g (i) be the set of directed bonds (i, j) which emanate from the vertex i,and...

Ngày tải lên: 07/08/2014, 06:23

... circular permutations are reducts of homogeneous structures over finite relational languages? Note that, analogous to the N-free permutations, there is a class of pentagon-free circular permutations ... classes of permutations defined below, J and J ∗ are trivial, J/ J ∗ and J ∗ /J are imprimitive, and U consists of all permutations. 3 The examples We begin by defining five classes of fin...

Ngày tải lên: 07/08/2014, 07:21

... essential cycle from ccw to cw. A flop is the converse of a flip, i.e., the reorientation of an essential cycle from cw to ccw. A flip sequence on X is a sequence (C 1 , , C k ) of essential cycles ... C is a simple directed ccw -cycle in X, then X C can also be obtained by a sequence of reversals of essential cycles from ccw to cw. Moreover, the set of essential cycles involved in su...

Ngày tải lên: 07/08/2014, 08:20