Báo cáo toán học: "On the number of permutations admitting an m-th root" pptx
Báo cáo toán học: "On the number of permutations admitting an m-th root" pptx
... in the case when m is prime.
Whether a permutation of
n
admits an m-th root can be read on the partition
of n determined by the lengths of the permutation’s cycles, because the class of such
the ... is the exponential generating function (EGF, formal series) of the
m-thpowersinthegroups
n
. This means that the number of m-thpowersin
n
is
p
n
(m)×n!foreachn....
Báo cáo toán học: "On the Number of Planar Orientations with Prescribed Degrees" pptx
... short proof of the factor theorem for finite graphs, Canadian
Journal of Mathematics, 6 (1954), pp. 347–352.
[38] W. T. Tutte, A census of planar triangulations, Canadian Journal of Mathematics,
14 ... from the source to the sink of ∆. We say that ∆ is a + triangle of B
if looking along the direct source-sink edge the triangle is on the left. Otherwise, if the
triangl...
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 ... can also be defined as the result of the insertion of the elements of a random permutation of
{1, ,n}into an initially empty tree.
Ascendants and d...
Báo cáo toán học: "On the number of perfect matchings and Hamilton cycles in -regular non-bipartite graphs" ppsx
... on a cycle other than C
1
. Each has
at least (d −4)n neighbours in C
1
and we can argue the existence of a 6-cycle as in the
previous case.
Remark: The proof shows that the number of Hamilton ... n)k
−1
φ(k).
In either case, the inequality in part 1 of the lemma holds.
On the number of perfect matchings and Hamilton
cycles in -regular non-bipartite graphs
Alan Fri...
Báo cáo toán học: " ON THE NUMBER OF FULLY PACKED LOOP CONFIGURATIONS WITH A FIXED" pot
... f
d
cannot be
the place of a notch, and the number of notches out of {f
1
,f
2
, ,f
d−1
} must be exactly
by 1 larger than the number of notches out of {e
1
,e
2
, ,e
d−2
}. An example of a choice
of notches ... 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...
Báo cáo toán học: "On the number of possible row and column sums of 0,1-matrices" pps
... (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 its entries, and
write |N| for the weight of ... of total degree at most n. This is true for the first term
N((λ
1
, ,λ
n−1
)) by the inductive hypothesis.
Each of the subsequent terms is itself a sum. By the inducti...
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 ... multiple of the other by an element of
the field. Let G
P
(q, d) denote the graph whose vertices are the points of P G(q, d) and two
(not necessarily d...
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 ... e-graphs, and point E
k+1
is the intersection of {E
1
, E
2
, . . . , E
k+1
} and the points of the other of the e-graphs.
Theorem 1. There can be at mo...
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 ... match as an edge.
Then an m-matching of P
k
is composed of m edges and k −2m vertices. Altogether k −m
objects. Hence the number of m-matchings...
Báo cáo toán học: "On the number of independent sets in a tree" pdf
... An interesting paper of Wagner [5] looks at the number of independent sets modulo m.
Wagner showed that the pr oportion of trees on n vertices with the number of independent
sets ... 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...