Báo cáo toán học: "The Insertion Encoding of Permutations" pot
Báo cáo toán học: "The Insertion Encoding of Permutations" pot
... the operation of Del
k
when
applied to the insertion encoding of π are precisely the insertion encodings of all the
permutations σ with σ π.
The proof of this lemma consists of an explicit, ... correspond to insertions of any type provided only that they can
be followed by further insertions leading to an element of L. The number of elements of L
of length n is the...
Báo cáo toán học: " The Translational Hull of a Strongly Right or Left Adequate Semigroup" pdf
... eρ
+
,andeρ
+
∈ E;
(ii) λ
+
e =(λe)
+
.
Proof.
(i) Since we assume that the set of all idempotents E of the semigroup S forms
a semilattice, all idempotents of S commute. Hence, λ
+
e =(λe)
+
e = ... set P (S) of all right translations) of the semigroup
S forms a semigroup under the composition of mappings. By the translational
hull of S, we mean a subsemigroup Ω(S) consisting...
Báo cáo toán học: "The Quantum Double of a Dual Andruskiewitsch-Schneider Algebra Is a Tame Algebra" pdf
... general-
ization of [7], of (A(n, d, μ, q))
∗cop
. Our main result is to give the structure of
projective modules of D(Γ
n,d
). By this, we give the Ext-quiver (with relations)
of D (Γ
n,d
)andshowthatD(Γ
n,d
) ... >
−
−1, the elements X
s
K
u,j
and
X
s
F
u,j
are linearly independent.
Proof. The proof of this lemma is same to the proof of Lemma 2.18 in [7]. For
completeness...
Báo cáo toán học: "The independence number of graphs with large odd girth" ppt
... independence number
of general graphs of a given odd girth. We shall prove some similar bounds to
those we prove for regular graphs in terms of a measure of the concentration of
edges.
Monien and ... for the independence
number in terms of the odd girth, but instead of the average degree of the graph
we have to use another measure of the concentration of edges.
8
Reference...
Báo cáo toán học: "THE INDEPENDENCE NUMBER OF DENSE GRAPHS WITH LARGE ODD GIRTH" ppsx
... cycles. Let
¯
d be the average degree of
vertices of G.Then
α(G) ≥
n
¯
d/2.
Proof. Since G contains no 3 or 5 cycles, we have α(G) ≥ d
1
(v) (consider the neighbors
of v)andα(G) ≥ 1+d
2
(v) (consider ... 2
−
(
k−1
k
)
n
k−1
k
d
1
k
.
Proof. Immediate from Theorem 3.
This improves Denley’s Theorem 4.
References
1. Denley, T., The Independence number of graphs with large odd girth, Th...
Báo cáo toán học: "The asymptotic number of set partitions with unequal block sizes" pot
... values of n, we shall use elementary estimates and some well-known bounds
for ordinary partitions (of a number) to express most values of b
n
in terms of the number
of ordinary partitions of k ... the number of partitions of (the number) n,andQis its ordinary
generating function. Also, define p(n, k) to be the number of partitions of n with largest
part at most k. We will ha...