Báo cáo toán học: "On hypergraphs with every four points spanning at most two triples" ppsx
Báo cáo toán học: "On hypergraphs with every four points spanning at most two triples" ppsx
... 6), such that
every four points span 0 or 2 edges, has at most 10(m/6)
3
edges (their result is quite a bit
stronger, but this version suffices for our purposes). We will use this on subhypergraphs
of ... proving that a positive proportion of quadruples contribute
to q
1
. By (1) this immediately lowers the bound of 1/3. Our primary tool is a result of
Frankl and F¨uredi [4] stating t...
Báo cáo toán học: "On Hypergraphs of Girth Five" pdf
... girth at least three, which states that an
r-graph, without a pair of sets intersecting in at least two points, has at most
n
2
/
r
2
edges, and the equality is attained for each r ≥ 3 and ... probability that the number of cycles of length at most four in H
is at least
1
4
r
−4r/3
n
4/3
is less than
1
2
. Therefore, with positive probability, H has at least
1
2...
Báo cáo toán học: "On graphs with cyclic defect or excess" docx
... graph Γ with defect 2, if there are at least 2 paths of length at most D(Γ) from
a vertex v to a vertex u, then we say that v is a repeat of u (and vice ve rsa) . In this
case we have two repeats ... we show that cos α must be an
algebraic integer of degree at most 4. We then note that if, for a given d and an eigenvalue
λ, Equation (9) has at least two values of k, then α m...
Báo cáo toán học: "On the Continuity of Julia Sets and Hausdorff Dimension of Polynomials" ppsx
... such that U ⊂ F (f
n
), ∀n 0. Since the Fatou set
is totally invariant, we can replace x with a finite iteration f
i
(x) at any stage of
the argument.
For each x ∈ F (f ), under iterating f
i
(x) ... compatible with dynamics; see
[4]. This means that for each c ∈ B
σ
(c
0
)themapj
c
: ω(0) → C is injective and
for each z ∈ ω(0) the function c → j
c
(z) is holomorphic. Being compatible...
Báo cáo toán học: " ON THE NUMBER OF DESCENDANTS AND ASCENDANTS IN RANDOM SEARCH TREES" ppsx
... the
recurrence relations for the analyzed quantities translate to equations over generating functions in
a natural way, almost automatically.
THE ELECTRONIC JOURNAL OF COMBINATORICS 5 (1998), ... by
[X]=
(X−µ)
2
=
X
2
+
[X]− [X]
2
.
Since we will mostly deal with families of random variables, with two (n and j)orone(n) index,
we will systematically work with multivariate gener...
Báo cáo toán học: " On plethysm conjectures of Stanley and Foulkes: the 2 × n case" ppsx
... shape 2 × k,
filled with numbers from {1, ,n}. Consider the sum
∆
∈P
k
Γ⊥∆
τ
Γ
. We claim that
only τ
Γ
’s for Γ of type at most n−k appear in this sum. We also claim that the coefficient
of ... therefore we
can assume that a
Γ
≥ b
Γ
.ObservethatΓ
0
is the only horizontal tableau such that
(a
Γ
0
,b
Γ
0
)=(n, 0). Let T
a
be the collection of horizontal tableaux Γ with a
Γ
= a,and...
Báo cáo toán học: "On edge colorings with at least q colors in every subset of p vertices" ppsx
... (5)
Assume indirectly that there is a (p, q)-coloring of K
n
with at most h colors. From this
assumption we will get a contradiction.
Consider a fixed (p, q)-coloring of K
n
with at most h colors. We ... linear and quadratic orders of
magnitude, so for q
lin
≤ q ≤ q
quad
. In particular we show that that we can have at most
log p values of q which give a linear f(n, p, q).
In o...
Báo cáo toán học: " On generalized weakly directional contractions and approximate fixed point property with applications" potx
... generalized weakly directional contractions and
approximate fixed point property with applications
Wei-Shih Du
Department of Mathematics, National Kaohsiung Normal University,
Kaohsiung 824, Taiwan
Email ... approximate fixed point property [7] in K provided inf
x∈K
d(x, T x) = 0. Clearly,
F(T) = ∅ implies that T has the approximate fixed point property. A natural generalization of the
approx...
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