Báo cáo toán học: "New infinite families of 3-designs from algebraic curves of higher genus over finite fields" potx
Báo cáo toán học: "New infinite families of 3-designs from algebraic curves of higher genus over finite fields" potx
... New infinite families of 3-designs from algebraic curves
of higher genus over finite fields
Byeong-Kweon Oh
∗
Department of Applied Mathematics
Sejong University, ... Yang, An infinite family of 3-designs from Preparata
codes over Z
4
, Des. Codes Cryptogr. 15 (1998), no. 2, 175–181.
[6] T. Helleseth, C. Rong, K. Yang, New infinite families of 3-designs...
Báo cáo toán học: "New infinite families of almost-planar crossing-critical graphs" ppsx
... in infinite families of k-crossing-critical graphs? We positively answer
one half of his question in Theorem 3.1 and Proposition 2.1;
• namely we construct, for all k > 2, infinite families of ... communication and preprint of [2]) that typi-
cal constructions of infinite families of simple 3-connected k-crossing-critical graphs create
bounded numbers (wrt. k) of ver...
Báo cáo toán học: "New Bounds for Codes Identifying Vertices in Graphs" pdf
... given finite regular graph G =(V,E), let B = |B(v)| denote the size (indepen-
dent of its centre) of a ball of radius one; let C be an identifying code. Since C is a
covering of V ,thesphere-covering ... h3asacodeword: this
allows the degree of g5toincreasebyoneonly(ifwetakei4andi6ascodewords).
But then the covering of h2, f0andh0 requires an increase of the degree of g1ofa...
Báo cáo toán học: "An infinite family of non-embeddable Hadamard designs" potx
... design in the infinite
family has the collection of five blocks mentioned above then so do all other members
of the infinite family;
3) Give a design having the required collection of five blocks.
Theorem ... matrix ofa2-(v, k, λ)designisab × v matrix A = a
ij
,in
which a
ij
=1ifblocki contains point j and a
ij
=0otherwise.
3 Results
The strategy for establishing the existence of an...
Báo cáo toán học: "An Infinite Antichain of Permutations" ppsx
... partially ordered set of finite permutations ordered
by deletion of entries contains an infinite antichain. In other words, there exists an
infinite collection of permutations no one of which contains ... y
i
for 1 ≤ i ≤ k ) are finite. (See p. 135 of [1]). Another
basic result is that all antichains of the partially ordered set of the finite words of a finite
alp...
Báo cáo toán học: " Extremal infinite overlap-free binary words" potx
... prefix of x of length 5.
Proof. Firstnotethatthewordyis necessarily overlap-free by assertion 1 of Lemma 2.
The existence of the decomposition for finite words is proved in [10], in the proof of
Theorem ... 10, and we extend it to infinite
words by continuity. The infinite fixed point of µ beginning with 0 is denoted by t, hence
t = 0110100110010110 ···.
The infinite fixed poin...
Báo cáo toán học: " New Bounds for Union-free Families of Sets" potx
... must consist of non-overlapping groups
of terms of the product
n
j=1
k
=1
q
j
. Hence we have
m
i=1
n
j=1
σ
j
(x
ij
) ≤
n
j=1
k
=1
q
j
=1.
The rest follows from the arithmetic-geometric ... contribute
tn
sn
triples. Fix a value of t which contributes at least
1
n
of the triples. Let 2
βn
be the number of pairs of subsets of F with intersection
of...
Báo cáo toán học: "Another infinite sequence of dense triangle-free graphs" docx
... structural
properties and that the natural way to describe the structure of these graphs
is in terms of graph homomorphisms. One infinite sequence of cores of dense
maximal triangle-free graphs was known. All graphs ... 4-colourable, in contrast to a conjecture of Jin [8], saying that there
are graphs of arbitrarily large chromatic number with this property.
Another infinite seq...
Báo cáo toán học: "Decomposing infinite 2-connected graphs into 3-connected component" pps
... accumulation points of infinite planar graphs, we generalize
Tutte’s decomposition to include all infinite 2-connected graphs.
1 Introduction
In [5], Tutte presents a decomposition of a finite 2-connected ... concerning accumulation points of infinite graphs embedded in
the plane provides motivation for generalizing Tutte’s decomposition to infinite graphs.
Question 1 Which (loca...
Báo cáo toán học: "New directions in enumerative chess problems to Richard Stanley on the occasion of his 60th birthday" docx
... of the authors of [CEF], to show this enumeration in helpmate form.
Each of the next two problems shows an infinite sequence: the n-th term of the sequence
is the number of ways White ... to many other kinds of mathematical
chess problems. Thanks too to Tim Chow, one of the organizers of the conference, for
soliciting the presentation and proofreading a draft of this articl...