Báo cáo toán học: " Value-Peaks of Permutations" pdf

... last claim in the theorem. 9 Proofs of Theorems 1 and 2 All mentions of Run(···) in Theorem 1 are divided by factorials and so can be thought of as functions of the form f(∗, ∗,γ) according to ... electronic journal of combinatorics 10 (2003), #R40 10 Asymptotics of Permutations with Nearly Periodic Patterns of Rises and Falls Edward A. Bender Department of Mathematics Univers...

Ngày tải lên: 07/08/2014, 08:20

... Classification of solutions for an integral equation. Comm. Pure Appl. Math. 59, 330–343 (2006) Nonexistence of positive solutions of an integral system with weights Zhengce Zhang School of Mathematics ... some assumptions of p, q, α, and β. Furthermore, using Doubling Lemma indicated in [14], which is an extension of an idea of Hu [15], Chen and Li [16, Theorem 4.3] obtained the...

Ngày tải lên: 20/06/2014, 21:20

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Ngày tải lên: 05/08/2014, 09:46

... the proof, we speak of the probability of various events, and evaluate the expected value of some random variables. The underlying probability space for all this is the set of all t-tuples of embeddings ... in terms of random embeddings of pairs of graphs in K n . Theorem 1, discusses random embeddings of t-tuples of graphs. In Theorem 2, we use this to extend Tomescu’s re...

Ngày tải lên: 07/08/2014, 06:20

... All squares of column −59 and row 59 of Q 119 are covered, so a copy of Q 118 is dominated. the electronic journal of combinatorics 8 (2001), #R29 16 Values of Domination Numbers of the Queen’s ... squares of these orthogonals are not covered by the required lines for a 0-cover D of size 2k + 1 for Q 4k+1 with e = f + 2; since the set of required lines of D is symmetric ac...

Ngày tải lên: 07/08/2014, 06:22

... cl(G) (the clique number of G). A set of vertices of a graph G is said to be independent if every two of them are not adjacent. The cardinality of any largest independent set of vertices in G is denoted ... edges. The vertex set and the edge set of a graph G will be denoted by V (G)andE(G), respectively. We call p-clique of G any set of p vertices, each two of which are ad...

Ngày tải lên: 07/08/2014, 06:23

... give a constructive proof of an equivalent restatement of Propo- sition 2.5, by looking at the circular classes of permutations τ ∈ S n which fix n. Note that the statement of Proposition 4.4 ( ... number of permutations σ ∈ S n with maj(σ) ≡ i (mod k)andmaj(σ −1 ) ≡ j (mod ). We give a combinatorial proof of: Theorem 3.1 Let  be a divisor of n − 1,=1, and let k be a divisor...

Ngày tải lên: 07/08/2014, 06:23

... 2. 3 Proofs of the first two Propositions Proof of Proposition 1. This proof relies on this simple standard algorithm for con- verting a list of all partitions of { 1, ,n} into a list of all partitions ... partitions of { 1, ,n+1}: 1. To each partition of { 1, ,n}, add the 1-member-set { n +1} as a new block. This gives a list of some of the partitions of { 1, ,n+1}. 2. To...

Ngày tải lên: 07/08/2014, 13:21

... one of type S × T, and (c) the assumption of having different sets ensures sufficiently many entries in both colors. We are now in the position to prove the second part of Theorem 3. Proof of Theorem ... respect to χ. Proof of Lemma 7. The proof is based on an argument from Ramsey theory. First we verify the statement of Lemma 7 for a fixed simplex. Then, by induction over the number...

Ngày tải lên: 07/08/2014, 13:21

... ANR-05- BLAN-0029-01. Appendix A. Proof of symmetry under interchange of spectral parameters The purpose of this appendix is to provide an explicit proof of the symmetry of the partition function of weighted plane ... center of the lozenge in such a way that the line of v forms an angle of +π/3 with that of u (contrary to the case of three little arches, we cannot get ri...

Ngày tải lên: 07/08/2014, 13:21