Báo cáo toán học: "Determinant expressions for q-harmonic congruences and degenerate Bernoulli numbers" ppt
Báo cáo toán học: "Determinant expressions for q-harmonic congruences and degenerate Bernoulli numbers" ppt
... combinatorics 15 (2008), #R63 16
Determinant expressions for q-harmonic congruences
and degenerate Bernoulli numbers
Karl Dilcher
∗
Department of Mathematics and Statistics
Dalhousie University, Halifax, ... [p]
q
), (1.4)
for primes p ≥ 3. More recently Shi and Pan [16] extended (1.3) to
H
p−1
(q) ≡
p − 1
2
(1 − q) +
p
2
− 1
24
(1 − q)
2
[p]
q
(mod [p]
2
q
),
for primes...
Báo cáo toán học: "RSK Insertion for Set Partitions and Diagram Algebras" pps
... of a standard tableaux T
λ
of shape
λ and vacillating tableaux P
λ
of shape λ and length 2k for some λ ∈ Λ
k
n
. Our bijection
uses jeu de taquin and RSK column insertion.
If T is a standard ... Dulucq and Sagan [DS]
extend this insertion to work for partial matchings (and other generalizations for skew
oscillating tableaux) and Roby [Ry2] shows that the growth diagrams also...
Báo cáo toán học: "Extremal problems for t-partite and t-colorable hypergraphs" ppsx
... x
j
= 0 for some j ∈ {1, 2, . . . , t}. Let a
k
= |V
k
|, a
j
= |V
j
|
and = x
k
a
j
a
k
/(a
j
+ a
k
). Define a new weighting x
by x
v
= x
v
for v ∈ V \(V
k
∪ V
j
),
x
v
= /a
j
for v ... x
v
for v ∈ V \(V
k
∪ V
j
),
x
v
= /a
j
for v ∈ V
j
and x
v
= x
k
− /a
k
for v ∈ V
k
. It is straightforward to check that
x
∈ S
p
and λ(G, x
) > λ(G, x), co...
Báo cáo toán học: "Graph Theory for Metric Dimension and Diameter" docx
... undirected, and simple. The vertex set and edge s et of a graph G
are denoted by V (G) and E(G). For vertices v, w ∈ V (G), we write v ∼ w if vw ∈ E(G), and v ∼ w
if vw ∈ E(G). For S ⊆ V (G), ... G
∗
∼
=
P
D+1
and for some k ∈ [2, D − 1], the vertices u
∗
k−1
and u
∗
k+1
of G
∗
are both not of type (1). Then u
∗
k−1
and u
∗
k+1
are both of type (N).
Proof. Let x and y...
Báo cáo hóa học: " Selection combining for noncoherent decode-and-forward relay networks" pptx
... Access
Selection combining for noncoherent
decode -and- forward relay networks
Ha X Nguyen
*
and Ha H Nguyen
Abstract
This paper studies a new decode -and- forward relaying scheme for a cooperative wireless ... is
thatasourcenodecooperateswithothernodes(or
relays) in the network to form a virtual multiple antenna
sys tem [1-7], hence providing spatial diversity. Amplify-
and- forward (...
Báo cáo toán học: "Meta-Fibonacci Sequences, Binary Trees and Extremal Compact Codes" pptx
... “greedy” algorithm for constructing a sequence of optimal
tree/codes for successive values of n and a fixed value h. We denote these trees T
n,h
for
natural numbers n and h and call them greedy ... t
h−1
.
Proof. For any h, the result is true for n = h + 1 since there is only one tree with h + 1
leaves and height h. Similarly it is true for n = 2
h
.
Assume the result is tr...
Báo cáo toán hoc:" Noncommutative determinants, Cauchy–Binet formulae, and Capelli-type identities " pptx
... See e.g. [12, 19, 30, 32, 37] for theorems of noncommutative linear algebra for
row-commutative matrices; and see also [32, secs. 5 and 7] for some beautiful q- and
q-generalizations.
the electronic ... noncommutative linear algebra for row-pseudo-commuta tive matrices
include Cramer’s rule for the inverse matrix [1 5, 31, 39] and the Jacobi identity for co-
factors [31],...
Báo cáo toán học: "Graphical condensation, overlapping Pfaffians and superpositions of matchings" pptx
... {b
i
, r
i
: b
i
and r
i
are of the same colour} =
e∈r
e
e
∪
e∈b
e
e
.
For an arbitrary graph H and subsets V
′
⊆ V(H) and E
′
⊆ E(H) introduce the notation
[H − V
′
− E
′
]
for the graph ... G, and let R = {r
1
, . . . , r
k
} and B = {b
1
, . . . , b
k
}. Le t
U := A ∩ (R
˙
∪ B) and V := B ∩ (R
˙
∪ B), and assume that |U| = |V |.
Let B
U
:= B ∩ U, B
V
:= B ∩ V...
Báo cáo toán học: "Unimodal rays in the regular and generalized Pascal pyramid" ppt
... now, that s
1
and s
2
are given, and then determine all positive divisor pairs
(s
3
, s
4
) such that s
3
s
4
= s
1
s
2
+ 1. Then the parameters s
i
and h
1
, h
2
generate u, n, t and
κ as above. ... + 6 − u and a
+
= n + 3t + 6 + u. Since both a
−
and a
+
are of the
same parity and a
−
a
+
is even, a
−
and a
+
must both be even. Thus a
−
/2 and a
+
/2 are
integers, one of t...
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