Báo cáo toán học: "Combinatorial interpretations of the Jacobi-Stirling numbers" pot
Báo cáo toán học: "Combinatorial interpretations of the Jacobi-Stirling numbers" pot
... be consistent with the model for the Jacobi-Stirling numbers of the first kind.
the electronic journal of combinatorics 17 (2010), #R70 4
Combinatorial interpretations of the
Jacobi-Stirling numbers
Yoann ... 1. The integer LS(n, k) is the number o f signed k-partitions of [±n]
0
.
By Theorems 1 and 2, we derive that the integer S(n, k) is the number of signed...
Báo cáo toán học: " Combinatorial Laplacian of the Matching Complex" pps
... dim E, the multiplicity
of the irreducible E
λ
in the c-eigenspace of Λ
E
r
equals the multiplicity of S
λ
in the c-
eigenspace of L
|λ|,r
.
Proof. Suppose |λ| =dimE. Then the c-eigenspace of L
|λ|,r
is ... to decompose all the eigenspaces of the
Laplacian into irreducibles and thereby decompose the homology. They also show that
the spectrum of the Laplacia...
Báo cáo toán học: "Combinatorial Identities from the Spectral Theory of Quantum Graph" potx
... orbits. In the present case a family
is completely specified by the integer q ≡ q
1
which counts the traversals of the loop 1,
i.e., the number of letters 1 in the code word. Each of these q letters ... operator
u
n
=trU
n
(19)
as sums of periodic orbits of the graph.
The two-point correlations in the spectrum of S (16) can be expressed in terms of the
average...
Báo cáo toán học: "Combinatorial Interpretations for Rank-Two Cluster Algebras of Affine Type." docx
... hand, the sum of the weights of the perfect matchings of G
n
is the poly-
nomial p
n
and the sum of the weights of the perfect matchings of H
3
is x
2
1
+ x
2
2
+ 1, so
the sum of the weights of the ... Bijective proof of Lemma 1
The recurrence of Lemma 1 can also be proven bijectively by computing in two different
ways the sum of the weights of...
Báo cáo toán học: " Further results of the estimate of growth of entire solutions of some classes of algebraic differential equations" docx
... g
m
(ζ))
b
a+deg
z,∞
a
r
m
{b
a+deg
z,∞
a
r
m
1
m
2
qk−p(r)
m
ρ
m
}
m
1
m
2
qk−p(r)
M
r
[g
m
](ζ).
(3.11)
11
3. Proof of the results
Proof of Theorem 1.4 Suppose that the conclusion of theorem is not true, then
there exists an entire solution w(z) satisfies the equation [Q(w(z))]
n
= ... C, if ζ is not the zero of g(ζ), by (3.4) then we can get g
(k)
(ζ) = 0 from (3.5).
By the...
Báo cáo toán học: "A Presentation of the Elements of the Quotient Sheaves Ωk /Θk in Variational Sequences" pdf
... in the theory of differential equations and
in mathematical physics.
Krupka [5] studied the sheaves of differential forms on finite r-jet prolonga-
tions J
r
Y . Then he constructed the sequence of ... 0.
1. Introduction
The notion of variational bicomplexes was introduced in studying the problem
of characterizing the kernel and image of Euler-Lagrange mapping in the ca...
Báo cáo toán học: "Further Applications of the KKM-Maps Principle in Hyperconvex Metric Spaces" pptx
... similarly. The proof is complete.
Now we are in a position to proof a version of the well known minimax
theorem due to Neumann-Sion [11, 15] in the case of hyperconvex metric spaces.
Theorem 3.5. ... Seminar
”Geometry of Banach spaces and Fixed point theory”, organized jointly by the Hanoi
Institute of Mathematics and Hanoi University of Education. The author would like...