Báo cáo toán học: "Restricting supercharacters of the finite group of unipotent" docx
Báo cáo toán học: "A Note on the Critical Group of a Line Graph" doc
... Further, in
the case in which the out-degree of each vertex of G is a fixed integer k, we show the
kernel of this surjection is the k-torsion subgroup of K(LG, e
∗
). These results appear
as Theorem ... exposition of the properties of the sandpile group, the reader is
referred to [2].
In his paper, [3], Levine shows that if e
∗
= (w
∗
, v
∗
), then κ(G, w
∗
) divides...
Báo cáo toán học: "Restricting supercharacters of the finite group of unipotent" docx
... = S
λ
, then a vertex of S sees u
1k
or u
jk
if and
only if either u
jk
is not South of the end of a tine but on a tine of S, or u
jk
is South
of the end of a tine and weakly North of the next ... subgroups of the
finite general linear groups GL
n
(F
q
); the group U
n
is the pattern group corresponding to
the total order 1 < 2 < 3 < · · · < n....
Báo cáo toán học: "A Note on the Symmetric Powers of the Standard Representation of Sn" ppt
... D(n).
Proof. Consider the table of the characters χ
N
; we are interested in the dimension
of the row-span of this table. Since the dimension of the row-span of a matrix is
equal to the dimension of ... well study the dimension
of the space spanned by the columns of the table. By the preceeding lemma, the
N
th
entry of the column corresponding to...
Báo cáo toán học: "A Note on the Asymptotic Behavior of the Heights in b-Tries for b Large" ppt
... bounded, then the height distribution
concentrates on two consecutive points.
3 Derivation of Results
We establish the five parts of Theorem 2. Since the analysis involves a routine use of the
saddle ... in the same way except that at
the k-th step, the splitting of sets is based on the k-th symbol of the underlying strings.
∗
This work was supported by DOE Grant DE...
Báo cáo toán học: "On cycles in the coprime graph of integers1" docx
... proof of Theorem 2.
2.2 Proof of Theorem 3
Here we assume that s
2
≥
2
n,thecases
1
≥
2
nis similar. Denote by P
r
the product of
the primes not exceeding r. The rough outline of the proof will ... G(A)forl>
n
6
.
In the proof we will distinguish two cases depending on the size of |A
(6,1)
| + |A
(6,5)
| .The
theorem will be an immediate consequence of the fo...
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: "A note on the edge-connectivity of cages" pdf
... subset of vertices (or
edges). The subgraph obtained from G by deleting the vertices in V
together with their
incident edges is denoted by G − V
. The graph obtained from G by adding a set of ... v)andd(u, X).
The length of a shortest cycle in a graph G is called the girth of G. Clearly, adding
edgestoagraphG might decrease the girth of G.IfG
is obtained from G by...
Báo cáo toán học: "ntersecting families in the alternating group and direct product of symmetric groups" potx
... fixing 1, . . . , r. Then the map φ : Γ(A
n
(1, . . . , r)) →
the electronic journal of combinatorics 14 (2007), #R25 4
Proof of Theorem 2.1. We shall imitate the proof of Theorem 4.2 in [8] by ... contradicting the maximality of I. So |I| = (m − 1)!m(n − 1)!. Again,
the maximality of I implies that m = n and so I has the required shape as above.
Proof of Theorem 1.4...
Báo cáo toán học: "Updown numbers and the initial monomials of the slope variety" ppsx
... x
i
) ∈ C be the slope of ℓ
ij
. Let A = C[m
ij
], and let
I
n
⊂ A be the ideal of algebraic relations on the slopes m
ij
that hold for all choices of the
points p
i
. Order the variables of A lexicographically ... upd own (or Euler)
numbers, thereby obtaining a formula for the number of generators of the initial
ideal of I
n
in each degree.
The symbol N will den...
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