Báo cáo toán học: "Symmetric Simplicial Pseudoline Arrangements" ppsx
Báo cáo toán học: "Ultraweakly closed operator algebras " ppsx
... class="bi x1 y1 w3 h 2" alt =""
Báo cáo toán học: " PROBLEMS IN ALGEBRAIC COMBINATORICS" ppsx
... square-counting or an interlacing argument, one can show that the max-
imum number of vertices in an independent set in the Hoffman-Singleton graph is 15. If
S is an independent set of size 15 in this ... Then H is the Hoffman-Singleton graph.
Note that we may view the vertices in S as points and the vertices not in S as lines,
with a point and line incident if the corresponding verti...
Báo cáo toán học: " Symmetric Sum-Free Partitions and Lower Bounds for Schur Numbers" potx
... and the second follows from (2)
and the bounds for R
5
(3) given in S. Radziszowski’s survey paper [6]. For earlier
work on lower bounds for S(k) see H. Fredricksen [5] and A. Beutelspacher and
W. ... D
k
(n)tobethemaximumofD(P )overall
symmetric sum-free partitions P of [1,n]intok sets. Notethatwemusthave
D
k
(n) ≤ S(k − 1) + 1.
Symmetric Sum-Free Partitions...
Báo cáo toán học: "On rainbow arithmetic progressions" ppsx
... 3
q
}. This coloring is easy to show not to have any rainbow arithmetic
progressions of length at least 3.
It turns out that in order to force a rainbow AP(k) we need to ensure that for each
color ... A
5
and i is odd,
C otherwise.
(4)
the electronic journal of combinatorics 11 (2004), #R1 6
On rainbow arithmetic progressions
Maria Axenovich
Department of Mathematics
Iowa State Uni...
Báo cáo toán học: "Packing densities of patterns" ppsx
... symbol of σ.Sincen +1>m, we can select a random subsequence
of σ of length m by first throwing out one of the n + 1 symbols of σ at random and
then randomly selecting a subsequence of length ... the following theorem of
Stromquist. We give a proof which is somewhat shorter than the proof in [1], both
for its own interest and because we will reuse the method of proof when stu...
Báo cáo toán học: "Matchings Avoiding Partial Patterns" ppsx
... 05A05, 05C30
Abstract
We show that matchings avoiding a certain partial pattern are counted by the 3-
Catalan numbers. We give a characterization of 12312 -avoiding matchings in terms
of restrictions ... decompose a 12312 -avoiding
matching into smaller 12312 -avoiding matchings. For notational convenience, we denote
by E
j
the edge (i, j) with i < j.
Lemma 2.1 Let M be a 12312 -avo...
Báo cáo toán học: "Symmetric Simplicial Pseudoline Arrangements" ppsx
... of
symmetric simplicial pseudoline arrangements constructed from the mirrors of a regular
k-gon and three additional symmetry classes of pseudolines. Finally, Section 6 discusses
symmetric simplicial pseudoline ... of simplicial pseudoline arrangements (also alluded to in [7]), but
details of these families have not been published.
This paper will produce several infinite families...
Báo cáo toán học: "Hereditary properties of tournaments" ppsx
... proof of Theorem 28 of [4] can also be adapted to hereditary properties of tour-
naments, to produce many properties with different exponential speeds, but we spare the
reader the details. Of ... proof of Theorem 1.
Lemma 7. Let P be a hereditary property of tournaments. If B(P) = ∞, then P contains
arbitrarily large structures of Type 1 or 2.
Proof. Let P be a hereditary pro...
Báo cáo toán học: "Saturation Numbers of Books" ppsx
... set X of b − 1 vertices, each of degree n − 1, a clique L of
p
2
vertices, a
the electronic journal of combinatorics 15 (2008), #R118 7
Saturation Numbers of Books
Guantao Chen
∗
Dept. of Math. ... has a set X of b−1
vertices, each of degree n − 1, a clique L of
p
2
vertices, a set T of n − p/2 − b + 1 vertices
inducing an almost (p − 1)-regular graph which contains a v...
Báo cáo toán hoc:" Saturation Numbers for Trees " ppsx
... [KT86]
Ta ble 2: Saturation Numbers for Trees of Order 7
Question 2: Can sharper bounds be established for Theorems 12 , 1 3, 16-19?
Question 3: For those classes of trees for which the saturation ... number.
Specifically, trees with long induced paths will have saturation numbers near the minimum
and trees with high values for δ
2
(T ) will have high saturation...
Báo cáo toán học: "Symmetric functions for the generating matrix of the Yangian of gln(C)" ppt
... 1
A
k
R
k,k+1
1
k
A
k
,
the electronic journal of combinatorics 16 (2009), #R128 3
Symmetric functions for the generating matrix
of the Yangian of gl
n
(C)
Natasha Rozhkovskaya
Department of Mathematics
Kansas ... to the terms of the sum, we conclude that each of them has the form
(−1)
m−k− 1
e
k
(u)p
−
m−k
(u − k),
and the Newton’s formula for eleme...
Báo cáo toán học: "Conjugacy of Coxeter elements" ppsx
... orienta tion.
4 Coxeter elements
A Coxeter word has one instance of each letter, so it defines an acyclic orientation of
the Coxeter graph. This orientation is in fact well defined by the Coxeter element, ... a corresponding Coxeter word.
So, Coxeter elements correspond bijectively to acyclic edge orientations of the Coxeter
graph. And we have seen that moving the first lette...
Báo cáo toán học: "Symmetric bowtie decompositions of the complete graph" ppsx
... divisor of p
n
− 1. If (v − 1)/q ≡ 0
(mod 12), then there is no bowtie decomposition of K
v
which is invariant with respect to
G.
Proof. We identify the vertices of the complete graph with the elements ... 1. The coset G − ρ consists
of the permutations on Z
v
of the form x → −x + i + 1. Each element o f G − ρ is a
reflection about the axis passing through th...
Báo cáo toán học: "Symmetric Laman theorems for the groups C2 and Cs" docx
... 4.1 Each of the constructions in Definitions 4.1 and 4.2 has the property that if
the graph G satisfies the Laman conditions, then so does
G. This follows from Theorems
2.2 and 2.3 and the fact ... − 4.
the electronic journal of combinatorics 17 (2010), #R154 39
proofs of the corresponding Laman- type t heorems for the groups C
2
and C
s
.
The Laman- type...
Báo cáo toán học: "Growth of graph powers" ppsx
... something of the form λr
with λ >
1
3
. To see this, consider the following sequence of graphs H
r
(d) as d tends
to infinity:
the electronic journal of combinatorics 18 (2011), #P88 5
Growth of graph ... increase in the number of edges of the cube of a regular, co nnected graph.
Such an increase was already demonstrated by Hegarty in Theorem 2. Here we give an
alternativ...
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