Báo cáo toán học: "A sharp bound for the reconstruction of partitions" ppt
Báo cáo toán học: "A sharp bound for the reconstruction of partitions" ppt
... agree above row r and to the left of column c (and the
definitions of r and c) we see that the only possibility for λ/µ is (r, c), completing the
proof of this case and the theorem.
Acknowledgements. ... 308, 9 (2008), 1524–1530.
the electronic journal of combinatorics 15 (2008), #N23 4
A sharp bound for the reconstruction of partitions
Vincent Vatter
Departme...
Báo cáo toán học: "A LOWER BOUND FOR THE NUMBER OF EDGES IN A GRAPH CONTAINING NO TWO CYCLES OF THE SAME LENGTH" pptx
... 1.
Then f(n) ≥ n +32t − 1, for n ≥ n
t
. This completes the proof of the theorem.
From the above theorem, we have
lim inf
n→∞
f(n) − n
√
n
≥
2+
2562
6911
,
which is better than the previous bounds
√
2(see[2]),
2+
487
1381
(see ... denote the number of vertices, and (G) denote the number of edges. In this
paper, we construct a graph G having no two cycles with the sa...
Báo cáo toán học: "A simple proof for the existence of exponentially balanced Gray codes" ppsx
... s
2
n
.
(1)
where b(i) is the number of times the integer i occurs in the sequence T . Note that the
sum of all b(i), 1 ≤ i ≤ n,isequaltol, the length of T .
3 A simple proof for the existence of exponentially
balanced ... code the transition counts of which
are all the same power of two, or are two successive powers of two. A proof for the
existence of e...
Báo cáo toán học: "A closed formula for the number of convex permutominoes" pot
... : the uppermost cell of the rightmost column of the polyomino has the maximal
ordinate among all the cells of the polyomino;
U2 : the lowest cell of the rightmost column of the polyomino has the ... interpretation of the closed formula (10) for the number of con-
vex permutominoes. We remark that the expression of f
n
resembles the expression
(1)...
Báo cáo toán học: "A short proof for the number of permutations containing pattern 321 exactly once" ppt
... exactly once.
In this paper, we give a short proof for the result of Noonan [3] that the number
of permutations of length n containing exactly one occurence of pattern 321 is
3
n
2n
n−3
.
(To be ... A short proof for the number of permutations
containing pattern 321 exactly once
Alexander Burstein
Department of Mathematics
Howard University
Washington, DC ... π
1
cπ...
Báo cáo toán học: "A Lower Bound for Schur Numbers and Multicolor Ramsey Numbers of K3" doc
... 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 ... defined to be the smallest integer
t
, such that in any k-coloring of the edges
of
K
t
, there is a complete subgraph
K
n
all of whose edges have the same color.
A su...
Báo cáo toán học: " A NEW CONSTRUCTION FOR CANCELLATIVE FAMILIES OF SETS" doc
... cancellative family of subsets of a n-set and f(k,n) to be the size of the largest
possible cancellative family of k-subsets of a n-set.
Note the condition A ∪ B = A ∪ C ⇒ B = C isthesameastheconditionBC ... denotes the symmetric difference.
Let F
1
be a family of subsets of a n
1
-set, S
1
.LetF
2
be a family of subsets of a n
2
-
set, S
2
. WedefinetheproductF
1
× F...
Báo cáo toán học: "A construction method for complete sets of mutually orthogonal frequency squares" pdf
... set of MOFS of
type F (km; k).
Proof. This is the case λ = 1 of the theorem.
Remark 3 Laywine proves the above corollary (see [1, IV.20.8(3)],[2] or [3]) for the
case when k is a power of m.
Corollary ... m.
Corollary 4 If there exists an affine plane of order m and complete set of type F (λm
2
; λ),
then there exists a complete set of type F (λm
2
; λm).
Proof. This is...
Báo cáo toán học: "An Asymptotic Expansion for the Number of Permutations with a Certain Number of Inversions" docx
... the asymptotic expansion of
B(n)/n!withO(n
−9/2
ln
19
n).
The following extension of Theorem 1 (the case m = 3) giving a complete asymptotic
expansion of I(n, x) can be immediately read out of ... (17)
where the last equation follows from (7). The error term in the first equation holds
uniformly for all real numbers x by the comments after (15) and, since | cos(ux)|≤1,...
Báo cáo toán học: "A natural series for the natural logarithm" pot
... presentation of the fundamental group of the knot complement. For a square matrix
M with entries in CG the trace tr
CG
(M) denotes the coefficient of the unit element in
the sum of the diagonal elements. The ... k
−2
AA
∗
)
n
(4)
The value of k can be chosen to be the product of (g −1)
2
and the maximum of the
1-norm of the entries in A (see [L¨uc94...
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