Báo cáo toán học: "Counting Pattern-free Set Partitions II: Noncrossing and Other Hypergraphs" ppt
Báo cáo toán học: "Counting Pattern-free Set Partitions II: Noncrossing and Other Hypergraphs" ppt
... 3k)inv the ith element and
the right element from the (k + 2)th, (k + 4)th, , 3k-th segment.) Thus w does not
Counting Pattern-free Set Partitions II:
Noncrossing and Other Hypergraphs
Martin ... parallel. Partitions, graphs, and other 12-free structures are usually
called noncrossing. Simion [21] gives a nice survey on noncrossing partitions. Before
proceeding to hyp...
Báo cáo toán học: "Counting Connected Set Partitions of Graphs" pot
... connected set partition of G belongs to one
of two classes:
(1) Set partitions that contain a block X with u ∈ X and v ∈ X.
(2) Set partitions for which u and v belong to different blocks.
Each set ... (2011), #P14 10
of blocks o f a set partition π is denoted by |π| and the set of all set partitions of X by
Π(X). The number of set partitio ns of a n n-element set...
Báo cáo toán học: "Minimally Intersecting Set Partitions of Type B" potx
... intersecting set partitions, we investi-
gate minimally intersecting set partitions of type B. Our main result is a formula for
the number of m inimally intersecting r-tuples of B
n
-partitions. ... the
type B Coxeter arrangements, see Bj¨orner and Wachs [3], Bj¨orner and Brenti [2] and
Humphreys [6].
A set partition of type B
n
is a partition π of the set {±1, ±2, . . . , ±...
Báo cáo toán học: "Records in set partitions" doc
... formulae for the number of set
partitions with a prescribed number of strong and additional weak records:
Theorem 2.1. The number of partitions of [n] with exactly k strong and ℓ additional
weak records ... block) and each element of B
1
other than the element 1 defines a singleton block.
The rest of the blocks remain unchanged. This mapping is an involution on the set of
part...
Báo cáo toán học: " Music-aided affective interaction between human and service robot" pptx
... and acoustic expressions. In
particular, the proposed expression system produces an affective reaction in
searches an image through a set of facial features indicating color and shape,
and ... each experiment: neutral, happy, angry, and sad. We chose ‘angry’
and ‘sad’ as the most representative negative emotions, whereas 'neutral' and
'happy' were chosen...
Báo cáo toán học: "A note on graph coloring extensions and list-colorings" pptx
... 3notequaltoK
∆+1
and let P be
a subset of vertices with pairwise distance, d(P ), between them at least 8. Let each
vertex x be assigned a list of colors of size ∆ if x ∈ V \ P and 1 if x ∈ P .Weprove
that ... B
1
, ··· ,B
∆
and edges u
1
w
1
,
u
2
w
2
, ··· ,u
∆
w
∆
. It is easy to see that the maximum degree of G
1
is ∆ and G
1
is not equal
to K
∆+1
. Assign a list {1} to each verte...
Báo cáo toán học: "Decompositions of graphs into 5-cycles and other small graphs" ppsx
... be a simple graph with vertex set V and edge set E. The number of vertices of a
graph is its order.Thedegree of a vertex v is the number of edges that contain v and will
be denoted by deg
G
v ... order r (r ≥ 3) and edges.
In this paper we will prove similar results to the ones obtained by Erd¨os, Goodman
and P´osa and by Bollob´as for some special cases of graphs H of order 4...
Báo cáo toán học: "Counting set systems by weight" doc
... The following definitions and Propositions 2.1
and 2.2 make this idea precise.
We call two set partitions P and Q of [n] orthogonal if |A∩B|≤1 for every two blocks
A ∈ P and B ∈ Q. Q is an interval ... W (n) to be the set of all pairs (Q, P ) such that Q and P
are orthogonal set partitions of [n]andQ is moreover an interval partition. We define
a binary relation ∼ on W (n) b...
Báo cáo toán học: "Counting subwords in a partition of a set" potx
... the set of partitions. For instance,
Chen et al. [2], Klazar [7], Sagan [12], Mansour and Severini [9], and Jel
´
inek and Mansour
[6] have studied pattern avoiding partitions. In [8], Mansour and ... be o bta ined by finding the number of partitions which may be
expressed as in (1) for each i and j and then summing over all possible values of i and j.
And there are
j
m...
Báo cáo toán học: "Counting distinct zeros of the Riemann zeta-function" docx
... J
N(T),
and for 2 ≤ n ≤ J,
M
n
(T )=
n
2
3β
n−1
2
− β
n−2
− 2
n−J−1
β
J
−
1 − β
J
2
J−n+1
(K − J)
−
J−1
j=n
2
n−j−2
β
j
N(T )
and M
j
(T)=0otherwise. Then
∞
j=1
M
j
(T)=N(T)andfor0≤ ... 1)π
−
1
2
s
Γ(
1
2
s )and
ζ(s)istheRiemannζ-function. The zeros of ξ(s) and its derivatives are all located in the critical
strip 0 <σ<1, where s = σ + it.SinceH(s) is regular and...
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