... Determining Lower Bounds for Packing Densities of
Non-layered Patterns Using Weighted Templates
Cathleen Battiste Presutti
Department of Mathematics
Bryn Mawr College, Bryn ... bound and introduce a generalized method involving weighted templates as a
way for computing lower bounds for δ(π), the packing density of a non-layered pattern π.
Furthermore, we...
... Lower Bounds for Ramsey Numbers
It is amazing that the result of this section has not been observed for the 25 years
since [C] was published. Using this observation we will give 6 new lower bounds.
Currently ... prime, q,forwhich3
does not divide q − 1. This can be accomplished automaticly by using the procedure
pryme. By using the procedure res we produce all of the cub...
... Bertram-Kretzberg, T. Hofmeister, and H. Lefmann [3], which for a discretization of
the problem finds a triangle with area log n/n
2
for every fixed n; lower bounds on higher
dimensional versions of the problem, ... value for H
5
.Theyalso
improved the lower bound for H
7
.
In this note, and by using a simple implementation of simulated annealing and a further
optimization...
... Acknowledgment
The author thanks Prof. Yair Caro and Raphael Yuster for sending reference [7]. The
author also thanks Prof. Cheng Zhao for his advice.
References
[1] J.A. Bondy and ... result.
Theorem. Let t = 27720r + 169 (r ≥ 1), then
f(n) ≥ n +32t −1
for n ≥
6911
16
t
2
+
514441
8
t −
3309665
16
.
2 Proof of Theorem
Proof. Let t = 27720r + 169,r ≥ 1,n
t
=
6911
16
t
2
+
514441
8
t ....
... Upper bounds for µ(n, d) obtained by µ(n, d) nµ(n − 1, d)
Proof. For each i, a
i
|C| counts the number of pairs of permutations (φ, ψ) with φ, ψ ∈ C
and φψ
−1
∈ C
i
, or, equivalently, the sum for ... action of Iso(n) (see [4] for more infor matio n on invariants).
Theorem 6 (LP bound for permutation codes (Tarnanen,[15])). Let D be a subset of
{1, . . . , m} and E any s...
... approximately 3 dB
gain of SNR at 10
-10
of outage probability under the
symmetric channels.
Figures 2 and 3 are the comparison of the ergodic
capacity versus K. Due to the lower bounds of both PDF
and ... mutually, and
have presented the exact closed-form expression for
outage probability in integral form as well as the lower
bound. A more overall investigation of the TWOR-...
... 1994
Abstract
For k ≥ 5, we establish new lower bounds on the Schur numbers S(k)
and on the k-color Ramsey numbers of K
3
.
For integers
m
and
n
,let[
m, n
]denotetheset{
i
|
m
≤
i
≤
n
}.AsetSof
integers ... k-coloring of the edges
of
K
t
, there is a complete subgraph
K
n
all of whose edges have the same color.
A sum-free partition of [1
,s
] gives rise to a
K
3
-free edge...
... γ(n, δ) for n ≤ 16.
In Table 1 we give a list of values (or bounds) for γ(n, δ) when n ≤ 16. In
this section we justify the entries of this table. See Table 3 in Appendix A for a
summary of how ... proof.
Proposition 3.2.
(1) γ(n, n − 1) = γ
r
(n, n − 1)= 1for any n ≥ 1.
(2) γ(n, n − 2) = γ
r
(n, n − 2)= 1for odd n ≥ 2.
(3) γ(n, n − 2) = γ
r
(n, n − 2)= 2for even n ≥ 2.
Proo...
... approximations of the roots for
specific values of d are found easily, and so are the inverses of the roots of
smallest modulus giving us the entries of first line of table 2.
the electronic journal of combinatorics ... eight.
However, the determination of the asymptotic behavior of the number of
walks of finite memory is much easier.
We can use the automaton directly fo...
... entry in the table of values of γ(n, δ)in[2]
Acknowledgement We wish to thank Gordon Royle for providing Cayley tables for
the 14 groups of order 16 and Cayley graphs of groups of orders up to 31.
References
[1] ... }.
the electronic journal of combinatorics 7 (2000), #R58 17
5 Exact values of δ
3
(n) for small n.
In this section we give exact values of δ
3
(n) for 6 ≤...