Báo cáo toán học: "Permutation Reconstruction from Minors" pps

... ∈ M k (p)andq is obtained from p by deleting i − 2 entries from 1, ,i− 1 and not deleting i}, B = {q | q ∈ M k (p)andq is obtained from p by deleting i − 2 entries from 1, ,i− 1andi}, C = {q ... paper develops in three main directions – permutation reconstruction from multisets and sets of minors as well as permutation reconstruction from sets of minors within certain classes...

Ngày tải lên: 07/08/2014, 13:21

... Determining a Permutation from its Set of Reductions, Ars Combi- natoria, to appear. [3] John Ginsburg, personal communication. [4] M. Raykova, Permutation Reconstruction from Minors, preprint. [5] ... for permutation reconstruction is the unsolved conjecture of Ulam [6], which when translated into the language of graph theory, concerns the unique reconstruc- tion of a graph G from...

Ngày tải lên: 07/08/2014, 13:21

... subtracting 1 from any number that is between i and j and subtracting 2 from any number that is greater than j. Hence, we obtain p ⇓ i ⇓ (j − 1) = p ⇓ j ⇓ i (2.1) for any 1 ≤ i < j ≤ n. From the ... deleting n from p or from q to form t, and thus either (iii) or (iv) is satisfied. Finally, if both p and q contain the 2-cycle (1n), then again the remaining cycles are unchanged by r...

Ngày tải lên: 07/08/2014, 21:21

Ngày tải lên: 05/08/2014, 15:20

... of all the weights of all permutations with exactly one (132) pattern. By adapting the argument from Mikl´os B´ona’s paper [1] we easily see that Q(q, z, t) satisfies Q(q, z, t)=zP(q, zt,qt)Q(q,z, ... pretty continued fraction, and deriving a fairly explicit form for its numerator and denominator. First, from (3) we have that P (q, z, t)= 1 1−zP(q,zt, tq) , (5) the electronic journal of co...

Ngày tải lên: 07/08/2014, 06:20

... does not depend from the choice of z in ω, namely Q|z = Q[U \ ω]. Proof. Let r be the rank function of Q and let x be the singular element of ω.For every subtransversal S, disjoint from ω, the submodularity ... of Ω; (c) every circuit of Q is either included in X or disjoint from X. Proof. The equivalence of (a) and (b) readily follows from the definition. The equivalence of (b) and (c...

Ngày tải lên: 07/08/2014, 06:22

... < 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

... T 1 contains at least 4 leaves from (T ), or if T 1 contains at least 2 leaves from (T)andsome of them is not single. Clearly, a nice subtree can be obtained from T by deleting any leaf which ... and at least 2 of them are not single, then one of T 1 ,T 2 is nice again. Notice that any set Q from the lemma can be displayed in some width-3 branch- decomposition of (M, P) by Theorem 5...

Ngày tải lên: 07/08/2014, 06:23

... separations. the electronic journal of combina torics 10 (2003), #R37 13 From now we assume s ≥ 3. Sublemma 4.2. t k ≥ 2s − 2. Proof. From condition (ii),  s−1 i=2 n i ≥ 1 2 (s − 2)(s − 3) + k(s − 2). ... this case take all the permutations as the identity. From now assume s>0. Case 2. t 1 ≤ s + 1 is odd. In this case, let σ 1 be the permutation from Lemma 3(a). The effect is to re...

Ngày tải lên: 07/08/2014, 08:20

... the amount of flow that has to go from A to A. This amount is  v∈A α(v) −  v∈A β(v), The flow leaving A is constrained by the capacity of the cut, i.e., number of edges oriented from A to A in Z, this ... on the choice of three vertices a 1 ,a 2 ,a 3 in clockwise order from the outer face of G.The suspension dual G σ ∗ is obtained from the dual G ∗ by some surgery: The dual-vertex cor...

Ngày tải lên: 07/08/2014, 08:20