... row-span of this table. Since the dimension of the row-span of a matrix is
equal to the dimension of its column-span, we can equally well study the dimension
of the space spanned by the columns of the ... the reflection representation of a finite Coxeter
group. This is essentially what we are looking at. (The defining representation of S
n
consists of the dir...
... bounded, then the height distribution
concentrates on two consecutive points.
3 Derivation of Results
We establish the five parts of Theorem 2. Since the analysis involves a routine use of the
saddle ... of k. For purposes of
comparison, we repeat these results below.
Theorem 1 The distribution of the height of b-tries has the following asymptotic expan-
sions for...
... stationary dis-
tribution is the desired distribution. The transitions of the chain consist of selecting a
vertex uniformly at random and modifying the configuration only at the chosen vertex.
The ... theorem we formally define the Markov chain for the Glauber
dynamics. For the purposes of the proof, the chain is defined on the set of all subsets of
V , not ju...
... that all (4; g)-cages are 4-connected [9].
We shall often use the following theorem of Fu, Huang and Rodger.
Monotonicity Theorem. [4] If k ≥ 3and3≤ g
1
<g
2
,thenf(k; g
1
) <f(k; g
2
).
If ... + 1, then one can delete these two
vertices and add a perfect matching of k edges between their neighbors so as to obtain
anewk-regular graph with girth at least g. By the Monotonicity Th...
... specified shortly. The construction used in the proof is
similar but more involved than the one of the first part of the proof.
For the remainder of the proof we will implicitly condition on the event ... 2
For the remainder of this note we will follow the notation and steps of the proof of
Theorem 5.4 in [4, Ch. 5.2]. Therefore most of the details that...
... bit of one string is the complement bit of the corresponding bit of the other
string. In this note, we further study the property of complement strings for three-person
games. We prove that if the ... choosing the pair of strings 11 . . . 10
and 00 . . . 01. We call these two strings “complement strings”, since each bit of one string is the
complement bit of th...
... surjection K(LG, e
∗
) → K(G, w
∗
). Further, in
the case in which the out-degree of each vertex of G is a fixed integer k, we show the
kernel of this surjection is the k-torsion subgroup of K(LG, ... out-degree 1. Let κ(G, w
∗
) denote the number of
directed spanning trees rooted at w
∗
. It is a well-known consequence of the matrix-tree
theorem that the number of...
... the condition nP(|X
1
| > η
n
) ≤ c(log n)
ε
0
, 0 < ε
0
< 1 in theorem 1.1 of [12].
Remark 1.4. If EX
2
< ∞, then X is in the domain of attraction of the normal law. Therefore, the ... of random variables
in the domain of attraction of the normal law, we will show that the ASCLT holds under a fairly general growth
condition on d
k
= k
−1
exp(ln k)
α
),...
... (3)
When conditioning on the event C
P
0
, the random graphs of the resulting probability
space may contain edges only from within the edges that connect vertices of different
partitions of P
0
. The ... information on Maple) implementation of the downhill simplex function optimization
method (see [13] for a good description of the method and a C implementation) to...