Báo cáo toán học: " Sumsets of finite Beatty sequences " pps
Báo cáo toán học: " Sumsets of finite Beatty sequences." pps
... Finite Beatty sequences
The above vocabulary extends in the obvious way to finite binary sequences, and Proposi-
tion C provides information about finite Beatty sequences and finite Sturmian sequences.
If
w ... ∆S satisfies one of the conditions in (ii) of Propo-
sition 2.
5 Infinite periodic Sturmian sequences
Periodic Sturmian sequences arise as difference sequence...
Báo cáo toán học: " Generating of Minimal Unavoidable Sets" pps
... because all the words of the form
w =(ab)
n
, the number of which is infinite, avoid X.
Remark 1.1. When replacing in X awordu by an extention u
of it, the
possibility of avoiding X for any ... Rab abbba
Lab Rab bbbb
Generating of Minimal Unavoidable Sets 465
The proof of (c), (d), (e), (f) are similar.
We consider now some basic transformations on any finite set X ⊂ A
∗
.
L...
Báo cáo toán học: " EVALUATION OF TRIPLE EULER SUMS" ppsx
... expressed as a rational linear combination of products of single and double Euler
sums of weight n.
We define the weight of a product of Euler sums as the sum of the arguments appearing
in the product. ... combination of products
of double and single Euler sums. The proof involves finding and solving linear equations
which relate the different types of sums to each other. We al...
Báo cáo toán học: " Reconstruction of Partitions Oliver Pretzel" pps
... u.
The proof of our theorem now follows from a sequence of lemmas. The first lemma
shows in passing that small subpartitions of S(m) have no corners at all.
Lemma 2. Let (k, ) be a corner of u ∈ ... consists of a single group H, this being the stabilizer of some
given t ≥ 1points. Ifχ = χ
x
denotes the irreducible character of G which is afforded
by the partition x of n then th...
Báo cáo toán học: "Asymptotics of Some Convolutional Recurrences" pps
... using a con-
volution. It often seems difficult to determine the asymptotic behavior of such sequences.
In this not e we study the asymptotics of a general class of such sequences. We prove
∗
Research ... a product of the r eciprocal of binomial
coefficients, which satisfies the conditions of Theorems 1 and 2. A more general case of
interest is when f(n, k) takes the fo rm of th...
Báo cáo toán học: "Enumeration of Restricted Permutation Triples" pps
... (11)
3 Enumeration of m-tuples of Permutations
More generally, we may consider the m-tuples of permutations of S
n
with exactly k
occurrences of “ R
m
”. Denote by D(n, k) the number of such multiple ... expression of Ω in terms of g, which turns to be the
generating function displayed in the theorem.
Furthermore, letting x = 0 in (10), we deduce that the number of permutati...
Báo cáo toán học: "Hamiltonicity of k-Traceable Graphs" pps
... a proof of which is elementary and is
omitted.
Lemma 4.8 If S is an independent set of a path P , consisting of internal vertices of P ,
then |N
P
(S)| ≥ |S| + 1.
the electronic journal of combinatorics ... achment in C, i.e., A = N
C
(H
1
). Let U
be the set of successors of vertices of A on C, and let W be the set of predecessors of vertices
of A on C. We first note tha...
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 infini...
Báo cáo toán học: "An Infinite Antichain of Permutations" ppsx
... 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
alphabet are finite, where x<yif one ... partially ordered set of finite permutations ordered
by deletion of entries contains an infinite antichain. In other words, there exists an
infinite collection of permu...
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 sequenc...
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