Báo cáo toán học: "A Bijection between Atomic Partitions and Unsplitable Partitions" ppt

... ind exed by unsplitable partitions . Can and Sagan raised the qu estion of finding a bijection between atomic partitions and unsplitable partitions. In this paper, we provide such a bijection. 1 ... and unsplitable. Our bijection will be concerned with atomic partitions that are splitable and unsplitable partitions that are not atomic. In other words, we sh...

Ngày tải lên: 08/08/2014, 12:23

... a partition of n. Note that there is no required relationship between π λ 1 and π λ 1 +1 , between π λ 1 +λ 2 and π λ 1 +λ 2 +1 , and so on. For any W λ = W λ 1 ,λ 2 , ,λ k , define W ¯ λ i = W λ 1 ,λ 2 , ... W λ 2 ,λ 3 , ,λ k ,λ 1 to a unique π ∈ W λ 1 ,λ 2 , ,λ k , so this process gives a bijection between W λ 1 ,λ 2 , ,λ k and W λ 2 ,λ 3 , ,λ k ,λ 1 . Now we prove that inv(π...

Ngày tải lên: 07/08/2014, 13:21

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Ngày tải lên: 05/08/2014, 15:21

... partition V = I ∪K such that the subgraphs G[I] and G[K] of G induced by I and K are empty and complete graphs, respectively. In 1980, Burkard and Hammer gave a necessary condition for a spl ... is also true for any k ≥ 6andm>k+2. The proof of Theorem 10 is complete.  References 1. M. Behzad and G. Chartrand, Introduction to the Theory of Graphs, Allyn and Bacon, Boston, 1971....

Ngày tải lên: 06/08/2014, 05:20

... Cornu´ejols and Guenin (20xxa), Guenin (1998a), and Novick and Seb¨o (1995a) (qq.v.). (S(M), SG: M, G, I(Gen), O: Exp, Ref, Exr) G´erard Cornu´ejols and Bertrand Guenin 20xxa On ideal binary clutters and ... group) and “consistency” in vertex-signed graphs ,and generalizable work on two-graphs (the set of unbalanced triangles of a signed complete graph) and on even and odd po...

Ngày tải lên: 07/08/2014, 05:23

... lemma. Recursively obtain the trees T 1 = f(S 1 )andT 2 =f(S 2 )on{0, ,l−1} and {0, ,n−l} respectively, with e(T 1 )=a(S 1 )ande(T 2 )=a(S 2 ), and thus by Part 4 of the Decomposition Lemma e(T 1 )+e(T 2 )+(s n −s ∗ n )=a(S). 3. ... T 1 and T 2 obtained in Step 2 of the bijection. The relabelings T  1 and T  2 obtained in Step 3 are shown in Figure 5. The vertex r in 7 0 4 5 1 2 8...

Ngày tải lên: 07/08/2014, 06:22

... Arthur, equipped with a random coin and only modest (polynomial-time bounded) computing power and Merlin, who is computationally unbounded. Both Arthur and Merlin are supplied with a word x, and the goal ... Sons, Inc., 1992. [3] L´aszl´o Babai and Shlomo Moran. Arthur-merlin games: a randomized proof system, and a hierarchy of complexity classes. Journal of Computer and System...

Ngày tải lên: 07/08/2014, 06:22

... are P [w, z] ∪Q[w, z] ⊂ P ∪ Q and P [x, y] ∪ P ∗ [x, y] ⊂ P ∪ P ∗ and P ∗ [x, z] ∪ Q[x, z] ⊂ P ∗ ∪ Q. Each of these cycles has length at most 2k,sincethe paths P, Q and P ∗ each have length at ... length, then P ∪Q and P ∗ ∪ Q each have exactly one cycle. It follows that there is a path Q[w, z] ⊂ Q such that Q[u, x]=P ∗ [u, x]andQ[x, w] ∪Q[z, v] ⊂ P [x, v] ∪P ∗ [x, v] and Q[w, z] is...

Ngày tải lên: 07/08/2014, 08:22