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...

Ngày tải lên: 07/08/2014, 06:23

... 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...

Ngày tải lên: 06/08/2014, 05:20

... 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...

Ngày tải lên: 07/08/2014, 06:20

... 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...

Ngày tải lên: 07/08/2014, 08:22

... 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...

Ngày tải lên: 08/08/2014, 11:20

... (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...

Ngày tải lên: 08/08/2014, 12:22

... 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...

Ngày tải lên: 08/08/2014, 14:22

... 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...

Ngày tải lên: 07/08/2014, 06:20

... 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...

Ngày tải lên: 07/08/2014, 06:20

... 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...

Ngày tải lên: 07/08/2014, 06:22