Báo cáo toán học: "Proof of an intersection theorem via graph homomorphisms" docx
Báo cáo toán học: "Proof of an intersection theorem via graph homomorphisms" docx
... homomorphism, ¯α(H
n
) ≥ ¯α(H) for any graph H.
We now can present the proof of the theorem.
Proof: Firstnotethatifp =1/2thenµ
p
is the uniform measure and the theorem is
trivial because if a vector in ... measure on G
n
our theorem now translates precisely to
the statement ¯α(G
n
) ≤ p.
the electronic journal of combinatorics 13 (2006), #N6 2
Proof of an intersection theor...
Báo cáo toán học: "ANALYSIS OF AN ASYMMETRIC LEADER ELECTION ALGORITHM" docx
... into an infinite sequence of consecutive intervals I
0
,I
1
,
ANALYSIS OF AN ASYMMETRIC LEADER ELECTION
ALGORITHM
Svante Janson Wojciech Szpankowski
∗
Department of Mathematics Department of Computer ... asymptotics of the mean and the variance of the height.
The next Theorem 2 provides an asymptotic expression for the distribution of the
height. We close this section wi...
Báo cáo toán học: " Proof of the Alon-Tarsi Conjecture for n = 2r p" docx
... p). (4)
Proof.Let
G={(σ, σ, τ):σ, τ ∈ S
p
, 0τ =0}. (5)
G acts on FDLS(p). By Lemma 3, sgn(Lg)=sgn(L) for any L of order p and any
g ∈ G.LetRbe any set of representatives of the orbits of G in FDLS(p), ... journal of combinatorics 5 (1998) #R28 3
the G-isotopy class of L.TheG-autotopism group
G
(L)ofLis the stabilizer of L
in G. Clearly
|G| = |LG||
G
(L)| (3)
for any G<
n
and...
Báo cáo toán học: "Proof of the Razumov–Stroganov conjecture for some infinite families of link patterns" pdf
... According
to Theorems 1 and 4, Φ
a,b,c
is a polynomial of total degree ab+bc+ca, and a symmetric
polynomial of the {α
i
} of degree at most a in each, of the {β
i
} of degree at most b in
each, and of ... of symmetry under interchange of spectral parameters
The purpose of this appendix is to provide an explicit proof of the symmetry of
the partition function of weigh...
Báo cáo toán học: "Proof of the combinatorial nullstellensatz over integral domains, in the spirit of Kouba" docx
... purpose of the present
note to try to lay bare the basic mechanism of Kouba’s proof.
2 Proof of Theorem 2
The proof of the Theorem 2 will be based on the following simple lemma.
Lemma 3. Let R be an ... change in the
setting of integral domains.
the electronic journal of combinatorics 17 (2010), #N14 3
Proof of Theorem 2. Let R be an arbitrary integral domain and f ∈ R...
Báo cáo toán học: "Proof of the (n/2 − n/2 − n/2) Conjecture for large n" pps
... e(T ),
then T ⊂ G. Furthermore, for any x ∈ U
1
and any a ∈ X, we can map x → a;
alternatively, for any leaf y ∈
˜
U
2
and any b ∈ Y , we can map y → b.
Proof of Lemma 7.4 for trees with at least ... n. This general Theorem 3.3 is necessary for the proof of Theorem 1.9
and becomes useful if one wants to show that G ⊃ T
n
under a (slightly) smaller value of
ℓ(G).
Proof of Theorem...
Báo cáo toán học: "Asymptotics of generating the symmetric and alternating groups" docx
... claimed.
3 Asymptotic expansion
It remains to prove Theorem 1 and obtain an asymptotic expansion for t
n
= s
n
/(n!)
2
.Itis
possible that this can be done with a careful analysis of the series f
S
(Π
0
)=
Π
µ(Π)g
S
(Π)
since ... series
E(X):=
∞
n=0
n!X
n
and T (X):=
∞
n=1
n!t
n
X
n
.
Then Section 2 of [5] shows that E(X)=expT (X)andso
T (X)=logE(X). (1)
We shall apply a theore...
Báo cáo toán học: "Truncations of Random Unitary Matrices and Young Tableaux" docx
... certain standard and semistandard Young tableaux. We combine
our formula with a variant of the Colour-Flavour Transformation of lattice gauge
theory to give a combinatorial expansion of an interesting ... Colour-Flavour
Transformation of lattice gauge theory to give another formulation of Theorem 1, which
gives a combinatorial expansion for an interesting type of matrix inte...
Báo cáo toán học: "Combinatorics of the three-parameter PASEP partition function" docx
... number of right-to-left minima i of σ satisfying σ
−1
(N + 1) < i.
Proof. This just means that in (5) we can replace the statistic u with u
′
, and this can
be done via a simple bijection. For any ... point of view by exchanging the empty sites with
occupied sites. It can also be obtained from the Matrix Ansatz by using the transposed
matrices D
∗
and E
∗
and the transposed vectors...
Báo cáo toán học: "Toughness of Ka,t-minor-free graph" ppsx
... such graph of order n contains
a cycle of length Ω(log
h(a,t)
n).
1 Introduction
In this paper, all graphs are finite and simple. A graph H is a minor of a graph K if H
can be obtained from a subgraph ... existence of k-trees and the toughness of a graph,
Graphs Combin. 5 (1989) 201–205.
the electronic journal of combinatorics 18 (2011), #P148 6
Toughness of K
a,t
-minor-...