... note on the almost sure limit theorem for self-normalized
partial sums of random variables in the domain of attraction of
the normal law
Qunying Wu
1,2
1
College of Science, Guilin University of ... sequence of independent and identically distributed random variables in the domain of attraction
of a normal distribution. A...
... any
nonhamiltonian Burkard–Hammer graph is contained in a maximal nonhamil-
tonian Burkard–Hammer graph. So knowledge about maximal nonhamiltonian
Burkard–Hammer graphs provides us certain information about nonhamiltonian
Burkard–Hammer ... assume that all con-
sidered in this paper maximal nonhamiltonian Burkard–Hammer graphs G =
S(I ∪ K, E)haveδ(G)=|I|−k where |I|≥k...
... need only show
that no prefix of m
n
is an overlap.
First note that no prefix of m
n
is a square of length 12 or greater; otherwise the prefix of m
n
of length 6 reappears internally, i.e. m
n
contains ... m
j
, a contradiction since m
j
is overlap-free.
Since aab is a prefix of m
i
,f(aab)=aaf(b)isaprefixofm
j
. However, another prefix of
m
j
is aabaab. Thus one of f (b)andbaab i...
... 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 direct sum of the reflection representation ... have:
Proposition 1.2. dim F
n
= D(n).
Proof. Consider the table of the characters χ
N
; we are interested in the dimension
of the row-span of this table. Since t...
... A Note on Sparse Random Graphs and Cover
Graphs
∗
Tom Bohman
†
Alan Frieze
‡
Mikl´os Ruszinko
Đ
Lubos Thoma
ả
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, ... a constant κ<2/3, then it outputs a cover graph whp. Note
that the output graph will have whp girth equal to 4. On a related note we point to
[8] which surveys constructions of no...
... sharp estimates obtained by Kamath et al.
of the probability that no bin is empty after the random placement of the balls
and exploiting the relationship between the placement of balls and the rigid ... A note on the non-colorability threshold of
a random graph
Alexis C. Kaporis, Lefteris M. Kirousis, and Yannis C. Stamatiou
University of Patras
Departm...
... is (k, )-sum-free for k, ∈ N, k>,ifthere
are no solutions to the equation x
1
+ ···+ x
k
= y
1
+ ···+ y
in A. Denote
by SF
n
k,
the number of (k, )-sum-free subsets of [1,n]. Since the ... ρ). The main result of this
note says that if (k − )/ is small in terms of ρ, then the number of
(k, )-sum-free subsets of [1,n]isequalto(ϕ(ρ)+ϕ
r...
... with b fixed, for < /b> various ranges of < /b> k. For < /b> purposes of
< /b> comparison, we repeat these results below.
Theorem 1 The < /b> distribution of < /b> the < /b> height of < /b> b- tries < /b> has the < /b> following asymptotic < /b> expan-
sions for < /b> ... u − 1=O (b
−1/2
). We thus set u =1+x/
√
b and obtain
I =
e
b
b
b+ 1
b!
B
−
√
b
exp
b
lo...
... edge
connected then the expected length of a minimum spanning tree is ∼
n
r
ζ(3). If we
omit the edge connectivity condition, then it is at most ∼
n
r
(ζ(3) + 1).
1 Introduction
Given a connected ... first give a rather precise description
of mst(G).
Lemma 1 [1]
For any connected graph G,
mst(G)=
1
p=0
E(κ(G
p
))dp − 1. (3)
A note on random minimum length spanning trees
Al...
... B. E. Sagan, R. P. Stanley (Eds.), Mathematical Essays in honor of Gian-Carlo
Rota, Birkauser, Basel. 1998, pp. 111-129
[3] Z. G. Liu, Some operator identities and q-series transformation formulas, ... (13)
The proof is completed.
References
[1] G.E.Andrews,Ramanujan’s ”lost” notebook. I. Partial θ-functions, Adv. in Math. 41
(1981), 137-172 .
[2] W.Y.C.Chen-Z.G.Liu,Parameter augmentation f...
... Classifications: 05C55
Abstract
Two new bounds for multicolor Ramsey numbers are proved:
R(K
3
,K
3
,C
4
,C
4
) ≥ 27 and R
4
(C
4
) ≤ 19.
1 Introduction
We prove two new bounds for multicolor Ramsey ... Y
¯
0
¯
0
T
¯
1
T
¯
0
T
¯
0
T
¯
0
T
0
the electronic journal of combinatorics 12 (2005), #N14 2
A Note on Two Multicolor Ramsey Numbers
Alexander Engstrăo...
... Classification: 0 5A1 5
Abstract
For a certain graph obtained by adding extra vertices and edges to the triangular
lattice graph, Propp conjectured that the number of perfect matchin gs of such a
graph ... consider the set of all perfect matchings of G
n
. Define a relation R on this
set as follows: two perfect matchings have the relation R if and only if they have...