Báo cáo toán học: "Linear Recurrence Relations for Sums of Products of Two Terms" ppt
Báo cáo toán học: "Linear Recurrence Relations for Sums of Products of Two Terms" ppt
... electronic journal of combinatorics 18 (2011), #P170 13
Linear Recurrence Relations for
Sums of Products of Two Terms
Yan-Ping Mu
∗
College of Science, Tianjin University of Technology
Tianjin ... 05A19
Abstract
For a sum of the form
k
F (n, k)G(n, k), we set up two systems of equations
involving shifts of F (n, k) and G(n, k). Then we solve the systems by ut...
Báo cáo toán học: "A recurrence relation for the “inv” analogue of q-Eulerian polynomials" ppsx
... number
of σ in the symmetric group S
n
of degree n. We give an algebraic proof and a
combinatorial proof of the recurrence relation.
1 Introduction
Let S
n
denote the symmetric group of degree ... A recurrence relation for the “inv” analogue of
q-Eulerian polynomials
Chak-On Chow
Department of Mathematics and Information Technology,
Hong Kong Institute of Education,
10 Lo...
Báo cáo toán học: "The Garnir relations for Weyl groups of type Cn" pot
... element of wJ ∩ Ψ
−
can be of
the form −2e
i
for some i, and so −2e
i
∈ wJ
(2)
. Now, put −α
∗
= 2e
i
. Then by definition
of the set J
−α
∗
, all the elements of wJ
occur in J
−α
∗
except for the ... combination of the polytabloids
the electronic journal of combinatorics 15 (2008), #R73 13
The main object of this paper is to construct the Garnir relations in terms of t...
Báo cáo toán học: " Fixed point theorems for contraction mappings in modular metric spaces" pptx
... point of T, {ε
n
} is a
sequence of positive numbers for which lim
n→∞
ε
n
= 0, and {y
n
} ⊆ X
w
satisfies
w
λ
(y
n+1
, T y
n
) ≤ ε
n
for all λ > 0. Then, lim
n→∞
y
n
= x
0
.
Proof. For each ... Tu, so T u is a fixed point of T
N
. By the uniqueness of fixed
point of T
N
, we have Tu = u. Thus, u is a fixed point of T . Since fixed point of
T is also fixed point of T
N
, we...
Báo cáo toán học: "TIGHT UPPER BOUNDS FOR THE DOMINATION NUMBERS OF GRAPHS WITH GIVEN ORDER AND MINIMUM DEGREE" pdf
... 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.
Proof. For each of ... three of the two element A
v
’s that contain z and at least
three, that contain w. So it is clear that we cannot avoid having either two A
v
’s of
the form {x, z} and {y,w} or, of...
Báo cáo toán học: "Tight Upper Bounds for the Domination Numbers of Graphs with Given Order and Minimum Degree, II." pdf
... 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 ≤...
Báo cáo toán học: "Conjectured Combinatorial Models for the Hilbert Series of Generalized Diagonal Harmonics Modules" docx
... combinatorial
properties of these statistics, obtaining an explicit summation formula for their generating
function and giving bijective proofs of the equivalence of different pairs of statistics.
As before, these ... )
t
x
0
(f)
n
j=1
count(f,j). (21)
Proof. In light of formula (20) and its proof, we need only show that
h
1
(P )+h
2
(P )=x
0
(f) for all P ∈P
n,k,m
(f).
Recall...
Báo cáo toán học: " Vizing-like conjecture for the upper domination of Cartesian products of graphs – the proof" pot
... that every vertex of N ∪ P is adjacent to a vertex of D
.
Of course, some of the sets could also be empty for some dominating sets.
If A and B are two subsets of the vertex set of a graph we say ... denote the set of vertices of V (G) \ D
G
which
are adjacent to a vertex of D
G
but are not private neighbors of any vertex of D
G
.Set
D
G
= D
G
\ D
G
denotin...
Báo cáo toán học: "On an identity for the cycle indices of rooted tree automorphism groups" doc
... a formula due to G. Labelle for the summed cycle indices
of all rooted trees, which resembles the well-known formula for the cycle index of
the symmetric group in some way. An elementary proof ... method is widely used for graph enumeration problems – we refer to
[6] and the references therein for instance. For the application of this method, information
on the cycle indices...
Báo cáo toán học: "Constructive Upper Bounds for Cycle-Saturated Graphs of Minimum Size" doc
... As the set of spokes form an edge-cut of the graph W (n, 2k +3), such
a cycle must in fact use an even number of spokes. If the number of spokes used is four
or more then the number of vertices ... no cycle of length l
exists.
Lemma 4 For any edge e in the complement of W (n, 2k +3) and k ≥ 7, the graph
W (n, 2k +3)+e contains a cycle of length l =2k +3.
Proof: We divide the...