Báo cáo toán học: "On Catalan Trees and the Jacobian Conjecture" pdf
Báo cáo toán học: "On Catalan Trees and the Jacobian Conjecture" pdf
... standard(C) and the set of standard
marked Catalan trees by standard(C, ∗). The standard trees in C
4
are
, , , , .
One of the standard trees in CH
3
is
.
The standard tree representing the class [T ... those trees which are largest in their equivalence class as
standard trees, and use them as equivalence class representatives. We will de-
note the set of standard...
Báo cáo toán học: "On rainbow trees and cycles" ppsx
... 4
n
e
−d
1/2
n/8
= o(1).
4 Proof of Theorem 3
We will use the lop-sided Lov´asz local lemma as in Erd˝os and Spencer [3] and in Albert,
Frieze and Reed [1]. We state the lemma as
the electronic journal of ... and teeth-edges.
We state our theorem as
Theorem 3 If an edge colouring of K
n
is k-bounded and
ν
1
−2
2
> 16kn then there exists
a rainbow copy of every possible...
Báo cáo toán học: "On Hopfian and Co-Hopfian Modules" potx
... Z-endomorphism, therefore, there are
Im(f
n
)=Im(f
n+i
) and Ker (f
n
) = Ker (f
n+i
) for any positive integer n and
i. It is easy to prove that M is neither Noetherian nor Artinian.
Thus Noetherian and ... Co-Hopfian). In fact, the results can be extended to the following,
and the proof is the same, so we omit it.
Theorem 2.2. Let M be a left R-module.
(1) If M is generaliz...
Báo cáo toán học: "Self-describing sequences and the Catalan family tree" pps
... between the self-describing sequences and the Catalan
family tree.
Theorem 2. The full names of the members of the Catalan family are precisely the self-
describing sequences. In other words, they ... statements of the theorem are implied by Theorem 1 and the following lemma.
Lemma 1. If a is a member of the Catalan family then a = δa. Otherwise, a<δa.
Proof. T...
Báo cáo toán học: "On some Ramsey and Tur´n-type numbers for paths a and cycles" doc
... length
between the girth and the circumference.
Theorem 4 (Brandt, [3]) A non-bipartite graph G of order n and more than
(n−1)
2
4
+1
edges contains all cycles of length between 3 and the length of the ... value of n is 2k − 2. Then, the
left-hand side is equal to k
2
− 3k + 4 and the right-hand side is equal to k
2
− 3k +
13
4
,
so by Brandt’s theorem graph G
contains C...
Báo cáo toán học: "On Base Partitions and Cover Partitions of Skew Characters" pptx
... λ
2
and so forth.
The conjugate λ
c
of λ is the diagram which has λ
i
boxes in the i-th column.
For µ ⊆ λ we define the skew diagram λ/µ as the difference of the diagrams λ and
µ defined as the ... [A
2
].
4 The Cover Partition
In this section we use Remark 3.5 and [Gut1, Theorem 4.2] to determine for the ordinary
and the Schubert product of two characters and for s...
Báo cáo toán học: "On a Generalization of Meyniel’s Conjecture on the Cops and Robbers Game" potx
... pair (x, y) of vertices with x ∈ X and y ∈ N
A
s
(x). We
call x the head and y the tail of the pair. By the remark, the set A ∩ N(x) has at most
m elements, and property (2) ensures that |N
A
s
(x)| ... [5], and extends the result of the second author [10], which
establishes the above bound for s = 2, 4.
1 Introduction
The game of Cops and Robbers, introduced by No...
Báo cáo toán học: "On Vertex, Edge, and Vertex-Edge Random Graph" pot
... overview. For these random graphs, the randomness inhabits the vertices and the edges
reflect relations between the randomly chosen structures assigned to them.
Finally, there is a class of random graphs ... Random
chordal graphs can be defined by selecting random subtrees of a tree [18].
Notice that for these random graphs, all the randomness lies in the structures attached to
t...
Báo cáo toán học: " Disconnected vertex sets and equidistant code pairs" pdf
... 7
TheHammingschemeisself-dual,whichmeansthatthedualeigenvalues
coincidewiththeeigenvalues.Theyaregivenby(see[8]):
Q
δ,j
=
n
k=0
(
−
1)
k
(q
−
1)
j−k
δ
k
n
−
δ
j
−
k
forδ,j
∈{
0, ,n
}
.
TheautomorphismgroupofH(n,q)istransitiveoneachrelation,soTheo-
rem2.5givestheexactvalueofφ
δ
foralln,qandδ.
ExampleIfn=6andq=6,thenforj=0, ,6therespectivevaluesof
Q
4,j
are1,6,
−
9,
−
44,111,
−
9 0and2...
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