Báo cáo toán học: "On the number of possible row and column sums of 0,1-matrices" pps
Báo cáo toán học: " ON THE NUMBER OF DESCENDANTS AND ASCENDANTS IN RANDOM SEARCH TREES" ppsx
... JOURNAL OF COMBINATORICS 5 (1998), #R20 8
3. The number of descendants in random BSTs
The number of the descendants D
n,j
of the j
th
node of a BST of size n is recursively computed
as the number of ... define the number of descendants D
n,j
as the size of the subtree rooted at the j
th
node, so
we count the j
th
node as a descendant of itself....
Báo cáo toán học: "On the number of perfect matchings and Hamilton cycles in -regular non-bipartite graphs" ppsx
... +2)
ν
n!
ν!2
ν
completing the proof of part (a) of Theorem 1.
the electronic journal of combinatorics 7 (2000), #R57 5
Part 2 of the lemma follows from the chain of inequalities
1
φ(k)
≤
1
γ(k
0
)
≤
(β ... +2)
n
n!.
In both cases the bounds are “close” to the expected number of in the random graph
G
n,d
. The results here are strongly related to the result o...
Báo cáo toán học: "On the number of permutations admitting an m-th root" pptx
... algebra, the radical of an ideal I is the set of all elements
of the ring some positive power of which belongs to I; in the present situation, q(m)is
the positive generator of the radical of the ideal ... shows
the first thousand values of kappa, with m on the x-axis and κ
m
on the y-axis.
0.4
0.6
0.8
1
1.2
0 200 400 600 800 1000
Figure 1: The function m ...
Báo cáo toán học: " ON THE NUMBER OF FULLY PACKED LOOP CONFIGURATIONS WITH A FIXED" pot
... between the rhombus tilings in the statement
of the theorem and these semistandard tableaux.
Proof of Theorem 2.2. It should be observed that, due to the nature of the region
R(λ, d, h), there ... in
each of the mid-points of edges along the bottom-left side of the region, and as well in each
mid-point along the downward edges which form part of a notch on...
Báo cáo toán học: "On the number of possible row and column sums of 0,1-matrices" pps
... condition for x and y to be row and column sums of a matrix
is that they have the same weight.
Clearly, the row sums of a member of M are at most n.Conversely,ifx =(x
1
, ,x
m
)
and 0 ≤ x
i
≤ n,letR ... (5)
the electronic journal of combinatorics 13 (2006), #N8 5
3 Start of the proof
Let N = {0, 1, }. Define the weight of a matrix N to be the sum of it...
Báo cáo toán học: "On the number of orthogonal systems in vector spaces over finite fields" ppsx
... q
d
2
+k−1
q
k−1
. From (2.6) and (2.8), the number of copies of K
k
in E is
(1 + o(1))
|E|
k
k!
q
−
(
k
2
)
.
.
This implies that the number of the number of k-tuples of k mutually orthogonal
vectors ... J
n
q,d
is the all one matrix and I
n
q,d
is the
identity matrix, both of size n
q,d
×n
q,d
). Therefore, the largest eigenvalue of V is D
q,d
and
th...
Báo cáo toán học: "On the number of genus one labeled circle trees" doc
... K
1
and K
2
are identical, then the number of edges in K
1
and K
2
is
the same, thus the sum of the number of edges in K
1
and K
2
is even, and on the other hand
it is
n−2
2
). Therefore, in case
n−2
2
is ... intersection of {E
1
, E
2
,. . .,E
k+1
} and the points of one of the e-graphs, and point E
k+1
is the intersection of {E
1
, E
2
, . . . ,...
Báo cáo toán học: "On the Number of Planar Orientations with Prescribed Degrees" pptx
... either none or both of the edges.
Let c
G
be the number of 2-factors of G. Among the 2-factors of G
(k) let S denote
the set of those, which induce a 2-factor of G, and S
c
the other 2-factors. ... cos
πj
.
The number of perfect matchings of G
2k−1,2−1
− (2k − 1, 1) is sandwiched between
that of G
2k−2,2−2
and that of G
2k,2
. Therefore the a...
Báo cáo toán học: "On the Number of Matchings in Regular Graphs" pptx
... −m)!.
Multiply all these choices to get the numerator of the right-hand side of (4.10). Divide
this number of choices by the number of permutations of {1, . . . , rn} to deduce the lemma.
✷
Using the methods ... φ(G, 4) the number of 4-cycles appeared as the first structure in
the graph, apart from n and r, which affects the number of matchings. The m...
Báo cáo toán học: "On the number of independent sets in a tree" pdf
... to the
result in [1] that the Fibonacci numbers (of the paths) form a complete system of residues
if and only if m = t · 5
k
, t = 1, 2, 4, 6, 7, 14, 3
j
where k 0, j 1 .
2 The number of ... turn to the number of matchings in a graph. This is a lso known as the
Hosoya index, or the Z-index in mathematical chemistry. For a rooted tree T , let Z(T )
be the numb...