Báo cáo toán học: "n-Color partition theoretic interpretations of some mock theta functions" doc
Báo cáo toán học: "n-Color partition theoretic interpretations of some mock theta functions" doc
... definitions of mock theta functions and
their order the reader is referred to [6]. The object of this paper is to provide new number
theoretic interpretations of the following mock theta functions:
Ψ(q)=
∞
m=1
q
m
2
(q; ... aq
n+i
)
,
for any constant a.
We remark that Ψ(q) is of order 3 while the remaining three are of order 5.
Number theoretic interpretations of...
Báo cáo toán học: "Another infinite sequence of dense triangle-free graphs" docx
... structural
properties and that the natural way to describe the structure of these graphs
is in terms of graph homomorphisms. One infinite sequence of cores of dense
maximal triangle-free graphs was known. All graphs ... 4-colourable, in contrast to a conjecture of Jin [8], saying that there
are graphs of arbitrarily large chromatic number with this property.
Another infinite sequenc...
Báo cáo toán học: " The Redheffer matrix of a partially ordered se" doc
... 0-element) of the ζ-matrix of S byacolumnofall1’s.
By the argument of the preceding section, the permanent of R(S)isthenumberof
-chains in S that contain the 0 element. The permutations of [ |S|] ... element. Then the permanent of R is the number of chains of S that contain the 0
element, and the determinant of R is
x∈S
µ(0,x), where µ is the M¨obius function of S.
If t...
Báo cáo toán học: "Minimum Weight H-Decompositions of Graphs: The Bipartite Cas" doc
... b)-decomposition
of G is a partition of the edge set of G such that each part is either a single edge or
forms an H-subgraph. We assign a weight of b to each H-subgraph in the decompo-
sition and a weight of ... of
G is a partition of the edge set of G such that each part is either a single edg e or forms an
H-subgraph, i.e., a graph isomorphic to H. We allow partitions on...
Báo cáo toán học: "On Multivariate Chromatic Polynomials of Hypergraphs and Hyperedge Elimination" docx
... definition of f(π) given in the paper of
Dohmen et al [DPT03]. By abuse of notation, we write e ⊆ π to mean the vertex set of
e is a subset of some block of π. Finally, let k
1
(π) denote the number of ... corresponding to the partition of V into
singletons. It also has a maximum element, corresponding to partitioning V into the
vertex sets of the components of H.
Given...
Báo cáo hoa học: " Research Article Meromorphic Solutions of Some Complex Difference Equations" doc
... purpose of this paper is to present the properties of the meromorphic solutions of
complex difference equations of the form
{J}
α
J
z
j∈J
fz c
j
Rz, fz,where{J} is
a collection of ... with the basic notations of Nevanlinna’s value
distribution theory; see 1–3.
Recent interest in the problem of integrability of difference equations is a consequence
of the e...
Báo cáo toán học: " Regenerative partition structures Alexander Gnedin" ppt
... distribution of two random elements of the set of partitions
of m for some 0 ≤ m ≤ n, allowing a trivial partition of 0,
(b) on the left side π
n
−{X
n
} denotes the random partition of n − X
n
derived ... points of a uniform sample into clusters. Given R, define an interval
partition of [0, 1] comprised of gaps,thatisopenintervalcomponentsof[0, 1] \R,and
of individ...
Báo cáo toán học: "A partition of connected graphs Gus Wiseman" pps
... consists of all edges of G
with both ends in S.
We will use the symbols π and σ to denote set partitions. The notation π S means
π is a set partition of the set S. The length (number of blocks) of ... denoted by (π).
A set partition σ is called a refinement of a set partition π if every block of σ is contained
in some block of π.
To each graph G on V there correspond...
Báo cáo toán học: "A graph-theoretic method for choosing a spanning set for a finite-dimensional vector space, with applications to the Grossman-Larson-Wright module and the Jacobian conjecture" pdf
... states without proof that M(3, ∞)
m
= 0 for m ≥ 3 in ([11], Theorem 3.12). Our
proof of this in Theorem 4.3 below illustrates the use of Case 1 of Corollary 2.13. This
supplies a proof of J
n,[d]
for ... ([11], Proposition 3.11). Our proof of this
in Theorem 4.4 below is different and provides a second example of Case 1 of Coro llar y
2.13. This supplies a proof of J
n,[2]
for...
Báo cáo toán học: "Recognizing Graph Theoretic Properties with Polynomial Ideals" pdf
... times to the sum
of the entries of the i-th column o f A
G
1
B
P
. Thus, the sum of the entries of the i-th column
of A
G
1
B
P
is kb
i
.
Second, consider B
P
A
G
2
. The sum of the entries in ... problem of determining the automorphisms Aut(G)
of an undirected graph G. Recall that the elements of Aut(G) are those permutations
of the vertices of G which preserve edge adj...