Báo cáo toán học: "An entropy proof of the Kahn-Lov´sz theorem a" ppsx
Báo cáo toán học: "An entropy proof of the Kahn-Lov´sz theorem a" ppsx
... A proof of the Kahn-Lov´asz theorem
The entropy proof of the Kahn-Lov´asz theorem is complicated by the fact that there can
be edges of the graph (and a fixed matching) amongst the neighbors of ...
E
is
independent of the event {x
V
y}.
Proof. For any permutation of the edges of m, there is a permutation of V (G) inducing
it. Therefore, the unif...
Báo cáo toán học: "An elementary proof of the hook formula" ppt
... (5)
The proof of (3) is completely combinatorial, the proof of (4) uses nothing more than the
fundamental theorem of algebra, and the proof of (5) is a simple geometric argument.
Proof of (3). The ... hooks in the diagram of λ.
Many proofs of this fact have been given, of varying complexity. We present here
an elementary new proof which uses nothing mor...
Báo cáo toán học: "Two New Extensions of the Hales-Jewett Theorem" pdf
... regular
words (that is, elements of W
M
k
) 0-variable words, then the Hales-Jewett theorem
corresponds to the case n =0,t = 1 of Theorem 1.4.
Theorem 1.4 Let k, r, n, t ∈ N be given. There exists M = M(k, ... θ,as
required.
In our application of Theorem 2.8, we shall not utilize idempotence of φ.
Theorem 2.9 (See [FK, Theorem 2.1]. Also [HS, Theorem 2.23] or [M1, T...
Báo cáo toán học: " An efficient implementation of iterative adaptive approach for source localization" pptx
... depends on the ratio of
interelement spacing of the array to the wavelength. In
the case that the angle ambiguity occurs, we refer to
[14-16] for resolving the ambiguity.
The remainder of this article ... it
is believable that the number of the selected principle
components i n step (b) of Table 2 is equal to the num-
ber of the actual sources ; for lower SNR...
Báo cáo toán học: "An Asymptotic Expansion for the Number of Permutations with a Certain Number of Inversions" docx
... replace the o(n
−7/2
) error term in the asymptotic expansion of
B(n)/n!withO(n
−9/2
ln
19
n).
The following extension of Theorem 1 (the case m = 3) giving a complete asymptotic
expansion of I(n, ... example) that the b(n, k)
satisfy a central limit theorem with µ
n
=
n
2
/2andσ
2
n
= n(n − 1)(2n +5)/72 (see [2;
Theorem 1]). Bender [2; p. 109] remarks that the theore...
Báo cáo toán học: " An Eigenvalue Characterization of Antipodal Distance-Regular Graph" ppt
... A
D
be the adjacency matrix of Γ
D
.IfA
D
belongs to the algebra
generated by A, then A
D
= J −R(A), where R :=
r
2
P −
r
2
+1 and P is the alternating
polynomial of Γ.
P roof. The first part of the ... 1),
which concludes the proof of the theorem. ✷
For general k, the given bound (3
) is sharp. For instance, in [14] it was shown
that the alternating polynomial P (...
Báo cáo toán học: "An improved bound on the minimal number of edges in color-critical graphs" pot
... H(G) does not exceed
the number of connected components of its low-vertex subgraph L(G).
Proof of Theorem 1. Let L(G) and H(G) be the low-vertex and the high-vertex subgraphs
of G, respectively. ... ingredient of our proof is the following result of Stiebitz.
Lemma 3 ([5]) Let G be a k-critical graph containing at least one vertex of degree k − 1.
Then the number...
Báo cáo toán học: "Matrix-free proof of a regularity characterization" doc
... electronic journal of combinatorics 10 (2003), #R39 8
2.3 Proof of Theorem 1.5
Before proceeding to the proof of Theorem 1.5, we begin by describing the constants
involved, the setup we use and ... our proof of Theorem 1.5, we do not appeal to the matrix argument of Section 1.1.2.
We show G
2
=⇒ G
1
follows directly from an application of the Szemer´edi Reg...
Báo cáo toán học: "An Extremal Characterization of Projective Planes" pps
... when the first author was visiting the
Department of Mathematical Sciences of the University of Delaware, and when the second
author was visiting the Department of Mathematics of the University of ... this is the
case, and the proof of our lemma is finished.
Remark The end of the proof above requires ∆ ≤ n/4 + 1. One may wonder why then
in the stateme...
Báo cáo toán học: "An Extremal Property of Tur´n Graphs a" potx
... ends the
proof of Case 2, and of Theorem 1.
Acknowledgment
The authors are thankful to Sebastian Cioab˘a, Gary Ebert, and Qing Xiang for their
comments on the original version of our proof. ... in a graph with more that t
r
(n − 1) edges, and the proof of the
theorem will easily follow. Let u
i
be a vertex in A with the lowest degree. Then
d(u
i
) ≤
1
r + 1
r+1...