Báo cáo toán học: "On the Eulerian enumeration of involutions" pps
Báo cáo toán học: "On the Eulerian enumeration of involutions" pps
... is the purpose of the present work to fill this gap, and in the course of doing
so, we obtain the involution analogues of the corresponding results on permutations. The
point of departure of this ... des σ and maj σ denote respectively the number of fixed points, the number of
transpositions, the number of descents, and the major index, of σ, on the class...
Báo cáo toán học: "On the first occurrence of strings" ppsx
... of all cases, and the proof of the lemma.
Lemma 12 With all the hypothesis of the previous lemma except that l
n
(τ
) = 2, P (T
τ
=
N
3
) > 1/3.
Proof: By direct computation, we verify the ... τ ≥ 2
n
+ 2
n−4
. Then c is the fourth character of σ
2
, the fifth character of σ
2
equals
the first character of σ
2
, the sixth character equals the second, and so...
Báo cáo toán học: "On the Asymptotic Distribution of the Bootstrap Estimate with Random Resample Size" ppsx
... > 0), which completes the
proof.
Proof of Theorem 2.1.
If EX
2
< ∞ then s
2
n
→ σ
2
a.s. Therefore, the theorem follows if we show that
the conditional distribution of Y
∗
nN
n
converges ... replacing the unknown distribution by the empirical
distribution of the data in the definition of the statistical function, and then
resampling the data to obtain a Monte...
Báo cáo toán học: "On the Asymptotic Behavior of Solutions of a Nonlinear Difference Equation with Bounded Multiple Delay" pptx
... =min
1ir
m
i
, ˆm =
1
r
r
i=1
m
i
.
The proofs of the following theorems can be obtained similarly as the proofs
of Theorem 6.20.1, Theorem 6.20.2 in [1], so we omit them here.
Theorem 2. Assume that
xF ... further that
lim sup
x,y→∞
H(x, y)
x
< 1 − λ
∗
, (2.2)
Then every solution {x
n
}
∞
n=−m
of (2.1) is bounded.
Proof. The proof follows from applying the mean value t...
Báo cáo toán học: " On the Representation Categories of Matrix Quantum Groups of Type A" docx
... element of
M. The construction of the linear functional resembles the integral on the Hopf
algebra H given in the previous section. In fact, using the same method as in
the proof of Theorem 3.2 ... understand the comodule category over the corresponding Hopf algebra. The
pair (r, s), where r is the number of roots and s is the number of poles of P
∧
(t)
(se...
Báo cáo toán học: "On the Domination Number of a Random Graph" docx
... from the first of these results that the domination number of G(n, p) is no larger
the electronic journal of combinatorics 8 (2001), #R37 1
≥ (log n)( n)p
2
ε
2
+ n =
(log n)(
n)p
2
4
+
n := C.
Thechoiceofε ... concentration
for the domination number D
n
of the subgraph G(n, p)ofG(
+
,p), p fixed. Specifically,
we shall prove
Theorem 5 Consider the infinite random graph G(
+
,...
Báo cáo toán học: "On the crossing number of Km,n" potx
... defined in the same way as in the proof of Lemma 1.
Lemma 3 Let λ be the number of distinct pairs of elements of B having the same cyclic
ordering of edges incident on an element of A
. Then, if ... drawing of some K
5,z
and let t
0
be an element of the
partite F with z elements and let T be the set of all elements of F having the same cyclic
ordering of e...
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