Báo cáo toán hoc:"Generating functions for the number of permutations with limited displacement " ppsx
Báo cáo toán hoc:"Generating functions for the number of permutations with limited displacement." ppsx
... Symp. on Inform. Th., 2 008, pp. 1736-1740.
[3] T. Kløve, “Spheres of permutations under the infinity norm - Permutations with lim-
ited displacement, ” Reports in Informatics, D ept. of Informatics, ... be the permutation corresponding to the transposed
of B.
We start with A
0,0
. Let A
x,z
be the matrix we have after k − 1 steps. Let the first
row of A
x,z
be row n...
Báo cáo toán học: "Improved bounds for the number of forests and acyclic orientations in the square lattice" doc
... problems on
the square lattice L
n
. There the authors gave the following bounds for the asymp-
totics of f(n), the number of forests of L
n
,andα(n), the number of acyclic orienta-
tions of L
n
:3.209912 ... lim
n→∞
α(n)
1/n
2
.
The proof of the second equality is very similar; it relies again on the formula T(G
∗
; x, y)=
T (G; y, x), and the fact that...
Báo cáo toán học: "Symmetric functions for the generating matrix of the Yangian of gln(C)" ppt
... to the terms of the sum, we conclude that each of them has the form
(−1)
m−k− 1
e
k
(u)p
−
m−k
(u − k),
and the Newton’s formula for elementary symmetric functions e
m
(u, τ) follows.
The proof ... < 0. The Newton’s identities show that these matrices
are inverses of each other. Therefore, each minor of H
−
is equal to the complementary
cofactor of the transpo...
Báo cáo toán học: "Threshold Functions for the Bipartite Tur´n Property a" potx
... 5,
µ
2
∆
≥
n
t
4
p
2t
2
t
2
n
t
2
p
2t
2
ϕ(1, 1)
10
the electronic journal of combinatorics 4 (1997), #R18 6
2. PROOFS
Proof of the Theorem:
We have already provided a proof of the second part of the theorem using nothing
more ... uniformly places ζ zeros and z = n
2
− ζ ones among the entries
of the n × n matrix [the subscript u refers to the fact that the...
Báo cáo toán học: "Generating functions for permutations which contain a given descent set" pot
... ∈B
λ,µ
w
u
(T ). For example if
u = (1, 2, 3, . . .), then w
u
(T ) = w(T ) is just the product of the lengths of the bricks that
lie at the end of the rows of T . We have g iven w(T ) for each of the brick ... the cells
of O in the same o rder that we read the underlying permutations and look for the first
cell c such that either:
(i) c is labeled wi...
Báo cáo toán học: "Lower Bound for the Size of Maximal Nontraceable Graphs." pot
... f(n)=3n/2 for n ≥ 19 and for
n =6, 10, 11, 12, 13, 17. The values of f(n) for the remaining values of n are also given
in [7].
Let g(n) denote the minimum number of edges in a MNT graph of order ... in
the next section, to prove that a MNT graph of order n ≥ 10 has at least
3n−2
2
edges.
The first one concerns the lower bound for the number of edges of...
Báo cáo toán học: "Lower Bounds for the Size of Random Maximal H-Free Graphs" pdf
... δ. This proves the
claim.
(3) The proof is similar to the proof of Claim 4.8 (2).
(4) The proof is similar to the proof of Claim 4.8 (1).
the electronic journal of combinatorics 16 (2009), #R4 ... claim holds for d − 1. We prove the claim for d. Let S = (G
1
, G
2
, . . . , G
d
)
be the sequence of the labels of the nodes u
i
, i ∈ [d], along the path P ....
Báo cáo toán học: "A note on the number of (k, )-sum-free sets" potx
... Denote
by SF
n
k,
the number of (k, )-sum-free subsets of [1,n]. Since the set of
1
the electronic journal of combinatorics 7 (2000), #R30 7
Proof. We need to show that the left-hand side of (4) is ... sets,J.
Number Theory 68 (1998), 151–160.
[6] P.J.Cameron,P.Erd˝os, On the number of sets of integers with various
properties, in R. A. Mollin (ed.), Number...
Báo cáo toán học: "A note on the number of edges guaranteeing a C4 in Eulerian bipartite digraph" pot
... consisting of the rows i =1, ,|A
+
|
and the columns j =2ρn +1, ,n. Define β = |A
+
|/m. Figure 1 visualizes these terms.
Let c(s, k) denote the number of entries of M equal to k in the block M
s
for ... ,2ρn.Denotethisblock
M
2
.DenotebyM
3
the block consisting of the rows i = |A
+
|+1, ,m and the columns
j =1, ,ρn.DenotebyM
4
the block consisting of the rows i...
Báo cáo toán học: "A Note on the Number of Hamiltonian Paths in Strong Tournaments" ppsx
... v
n
→ v
1
and all other arcs are of the form v
i
→ v
j
with i<j. In other words,
reversing the arc v
n
→ v
1
gives the transitive tournament of order n. As noted by Moon
[1], there is a bijection ... satisfy the lemma. Let t be the number of strong components of T − v
and let W
i
be the set of vertices in the i
th
strong component. If |W
1
|≥3, then choose
a ver...
Từ khóa: