Báo cáo toán học: "Face numbers and nongeneric initial ideals" doc
Báo cáo toán học: "Face numbers and nongeneric initial ideals" doc
... J. Herzog, and T. Hibi. Shifting operations and graded Betti numbers.
J. Algebraic Combin., 12:207–222, 2000.
[3] D. Bayer, H. Charalambous, and S. Popescu. Extremal Betti numbers and applica-
tions ... parts 1 and 2
are [11, Lemma 6.3], and part 3 follows from Corollary 2.5 and Lemma 2.6 of [2].
In the rest of this section we discuss an application of Lemma 2.2 to the face...
Báo cáo toán học: "Updown numbers and the initial monomials of the slope variety" ppsx
... .)
Theorem 2. Let n ≥ 2, and le t a, b be words such that (a, b) ∈ S
n−1
. Then the word
(n+2, a, n, b, n+1) ∈ S
n+2
is a primi tive G-word if and only i f 1 ∈ b and both (n+1, a
∗
, n)
and (n + 1, b, ... and let P, Q be subsets of [n] such that
p = |P | ≥ 3, q = |Q| ≥ 3, P ∪ Q = [n], and P ∩ Q = {n − 2}.
Let x = (x
1
, a, x
p
) ∈ S
P
and y = (y
1
, b, y
q
) ∈ S
Q
such that x
p...
Báo cáo toán học: " Independence number and disjoint theta graphs" doc
... T
i
for some i. Let u and v be the hub
vertices of T and let Q
1
, Q
2
and Q
3
be the paths of T ea ch containing u and v.
Suppose u and v are each incident to at least one edge of E and, without loss ... T
i
for
some i. Let u and v be the hub vertices of T and let Q
1
, Q
2
, Q
3
be the three paths of T ,
each including u and v.
Suppose u and v are each incident to at leas...
Báo cáo toán học: "Stapled Sequences and Stapling Coverings of Natural Numbers" doc
... either four or five numbers.
If A
2
covers four numbers, then A
3
,A
5
and A
7
can cover not more than two
numbers, one number, and one number, respectively, out of five remaining
numbers, thus, leaving ... coverings, and to Prof. Lev B. Levitin for useful discussions and
comments. Special thanks are due to the referee for carefully reading the
paper and suggesting thoughtful imp...
Báo cáo toán học: "Generalizing Narayana and Schr¨der Numbers o to Higher Dimensions" doc
... the definitions of the
small and large Schr¨oder numbers (as seen in [24]): Let the small and large d-Schr¨oder
numbers, respectively, be the sequences (N
d,n
(2))
n≥1
and (2
d−1
N
d,n
(2))
n≥1
, ... i<dn}|.
Define the matrices M
A
and M
D
so
(M
A
)
j
:= 1 if j<, and = 0 if otherwise,
(M
D
)
j
:= 1 if j>, and = 0 if otherwise.
Hence, asc(P )=Θ
M
A
(P ) and des(P )=...
Báo cáo toán học: "Distinguishing numbers for graphs and groups" docx
... φ
O
and φ
X\O
. Consequently g
is in the subgroup Stab(O) ∩ Stab(X\O)andsog is in Stab(X).
This gives a numerical condition for 2-distinguishability.
Corollary 2.4. Suppose Γ acts on X and O
1
and ... x
1
∈ O
1
and x
2
∈ O
2
. Define a labelling φ : X −→ { 1, 2} by setting
φ(x
1
)=φ(x
2
)= 2and (x) = 1 for all other x.Ifg preserves φ then it satisfies
φ(g.x
1
)=2=φ(g.x
2
).
Since g.x
i...
Báo cáo toán học: "Total domination and matching numbers in claw-free graphs" doc
... Factors and Factorization. 403–430. Handbook of Graph Theory ed. J.
L. Gross and J. Yellen. CRC Press, 2003, ISBN: 1-58488-092-2.
[11] W. R. Pulleyblank, Matchings and Extension. 179–232. Handbook ... journal of combinatorics 13 (2006), #R59 9
Total domination and matching numbers
in claw-free graphs
1
Michael A. Henning
∗
and
2
Anders Yeo
1
School of Mathematical Sciences
Univers...
Báo cáo toán học: "Fixing Numbers of Graphs and Groups" pptx
... and fix(Γ) = {1, . . . , k}.
3.2 Symmetric groups
The inflation of a graph G, Inf(G), is a graph with a vertex for each ordered pair (v, e),
where v and e are a vertex and an edge of G, and v and ... that v and u are adjacent
vertices of Inf
k
(K
n
). By the definition of inflatio n, v = (v
′
, e
′
) and u = (u
′
, d
′
) for two
vertices v
′
and u
′
in Inf
k−1
(K
n
) and two edg...
Báo cáo toán hoc:" Permutation Statistics and q-Fibonacci Numbers " doc
... counted by the Fibonacci numbers. These distribu-
tions will give us q-Fibonacci numbers which are related to the q-Fibonacci numbers of
Carlitz [2], Cigler [3, 4], and Goyt and Sagan [6].
Let the ... where F
n
= F
n−1
+ F
n−2
and F
0
= 1 and F
1
= 1.
Let [n] = {1, 2, . . . n} and [k, n] = {k, k + 1, . . . , n}. We will call two integer sequences
a
1
a
2
. . . a
k
and b
1
b
2...
Báo cáo toán học: "Betti numbers of monomial ideals and shifted skew shapes" potx
... plane, but
rather inside the m × n rectangle with row and column indices given by X and Y .
On the other hand, given a shifted skew diagram D, and a linearly ordered subset X,
one can also form ... Eliahou and Kervaire [15] and Aramova, Herzog, and Hibi [1]. The answers
for I(F ) generalize Corollary 2.17.
Corollary 3.14 If K is a squarefree strongly stable d-uniform hypergraph,...