The existence of (p,q)-extended Rosa sequences

A (p,q)-extended Rosa sequence is a sequence of length 2n+2 containing each of the symbols 0,1,…,n exactly twice, and such that two occurrences of the integer j>0 are separated by exactly j-1 symbols. We prove that, with two exceptions, the conditions necessary for the existence of a (p,q)-extended Rosa sequence with prescribed positions of the symbols 0 are sufficient. We also extend the result to λ-fold (p,q)-extended Rosa sequences; i.e., the sequences where every pair of numbers is repeated exactly λ times.     

Optimal conflict-avoiding codes of length <Emphasis Type="Italic">n</Emphasis> ≡ 0 (mod 16) and weight 3

A conflict-avoiding code of length n and weight k is defined as a set of binary vectors, called codewords, all of Hamming weight k such that the distance of arbitrary cyclic shifts of two distinct codewords in C is at least 2k−2. In this paper, we obtain direct constructions for optimal conflict-avoiding codes of length n = 16m and weight 3 for any m by utilizing Skolem type sequences. We also show that for the case n = 16m + 8 Skolem type sequences can give more concise constructions than the ones obtained earlier by Jimbo et al.      

Incongruent restricted disjoint covering systems

We define an incongruent restricted disjoint covering system on [1,n] as a set of congruence classes such that each integer in the interval [1,n] belongs to exactly one class, and each class contains at least two members of the interval. In this paper we report some computational and structural results and present some open problems concerning such systems.     

On partitions of {1,…,2m + 1}\{k} into differences d,…,d + m − 1: Extended Langford sequences of large defect

It is shown that for m = 2d ? 1, 2d, 2d + 1, and d ≥ 1, the set {1, 2,…, 2m + 2}, ? {2,k} can be partitioned into differences d,d + 1,…,d + m ? 1 whenever (m,k) ≡ (0,0), (1,d + 1), (2, 1), (3,d) (mod (4,2)) and (d,m,k) ≠ (1,1,3), (2,3,7) (where (x,y) ≡ (u,ν) mod (m,n) iff x ≡ u (mod m) and y ≡ ν (mod n)). It is also shown that if m ≥ 2d ? 1 and m ? [2d + 2, 8d ? 5], then the set {1, 2, …, 2m + 1} ? {k} can be partitioned into differences d,d + 1,…,d + m ? 1 whenever (m,k) ≡ (0, 1), (1,d), (2,0), (3,d + 1) mod (4,2). Finally, for d = 4 we obtain a complete result for when {1,…,2m + 1} ? {k} can be partitioned into differences 4,5,…,m + 3. © 2004 Wiley Periodicals, Inc.     

Normal sequences over finite abelian groups

In this note, we obtain the structure of short normal sequences over a finite abelian p-group or a finite abelian group of rank two, thus answering positively a conjecture of Gao and Zhuang for various groups. The results obtained here improve all known results on this conjecture.     

Sequences in abelian groups G of odd order without zero-sum subsequences of length exp(G)

We present a new construction for sequences in the finite abelian group without zero-sum subsequences of length n, for odd n. This construction improves the maximal known cardinality of such sequences for r > 4 and leads to simpler examples for r > 2. Moreover we explore a link to ternary affine caps and prove that the size of the second largest complete caps in AG(5, 3) is 42.      

The spectrum of cyclic BSA(ν, 3, λ; α) with α = 2, 3

Balanced sampling plans excluding contiguous units (or BSEC) were first introduced by Hedayat, Rao, and Stufken in 1988. In this paper, we generalize the concept of a cyclic BSEC to a cyclic balanced sampling plan to avoid the selection of adjacent units (or CBSA for short) and use Langford and extended Langford sequences to construct a cyclic BSA(ν, 3, λ; α) with α = 2, 3. We finally establish the necessary and sufficient conditions for the existence of a cyclic BSA(ν, 3, λ; α) where α = 2, 3. © 2005 Wiley Periodicals, Inc. J Combin Designs.     

Kronecker–Halton sequences in Fp((X−1))

In this paper we investigate the distribution properties of hybrid sequences which are made by combining Halton sequences in the ring of polynomials and digital Kronecker sequences. We give a full criterion for the uniform distribution and prove results on the discrepancy of such hybrid sequences.     

二项式型自反多项式

In this paper, we define the self-inverse sequences related to sequences of polynomials of binomial type, and give some interesting results of these sequences. Moreover, we study the self-inverse sequences related to the Laguerre polynomials.     

Spectral Sequences on Combinatorial Simplicial Complexes

The goal of this paper is twofold. First, we give an elementary introduction to the usage of spectral sequences in the combinatorial setting. Second we list a number of applications.In the first group of applications the simplicial complex is the nerve of a poset; we consider general posets and lattices, as well as partition-type posets. Our last application is of a different nature: the -quotient of the complex of directed forests is a simplicial complex whose cell structure is defined combinatorially.     

Catalan-like number sequences and Hausdorff moment sequences

Many well-known Catalan-like sequences turn out to be Stieltjes moment sequences (Liang et al. (2016)). However, a Stieltjes moment sequence is in general not determinate; Liang et al. suggested a further analysis about whether these moment sequences are determinate and how to obtain the associated measures. In this paper we find necessary conditions for a Catalan-like sequence to be a Hausdorff moment sequence. As a consequence, we will see that many well-known counting coefficients, including the Catalan numbers, the Motzkin numbers, the central binomial coefficients, the central Delannoy numbers, are Hausdorff moment sequences. We can also identify the smallest interval including the support of the unique representing measure. Since Hausdorff moment sequences are determinate and a representing measure for above mentioned sequences are already known, we could almost complete the analysis raised by Liang et al. In addition, subsequences of Catalan-like number sequences are also considered; we will see a necessary and sufficient condition for subsequences of Stieltjes Catalan-like number sequences to be Stieltjes Catalan-like number sequences. We will also study a representing measure for a linear combination of consecutive terms in Catalan-like number sequences.     

Identities on Bell polynomials and Sheffer sequences

In this paper, we study exponential partial Bell polynomials and Sheffer sequences. Two new characterizations of Sheffer sequences are presented, which indicate the relations between Sheffer sequences and Riordan arrays. Several general identities involving Bell polynomials and Sheffer sequences are established, which reduce to some elegant identities for associated sequences and cross sequences.     

Strong characterizing sequences for subgroups of compact groups

In [A. Biró, V.T. Sós, Strong characterizing sequences in simultaneous Diophantine approximation, J. Number Theory 99 (2003) 405–414] we proved that if Γ is a subgroup of the torus R/Z generated by finitely many independent irrationals, then there is an infinite subset AZ which characterizes Γ in the sense that for γR/Z we have ∑_aAaγ<∞ if and only if γΓ. Here we consider a general compact metrizable Abelian group G instead of R/Z, and we characterize its finitely generated free subgroups Γ by subsets AG^*, where G^* is the Pontriagin dual of G. For this case we prove stronger forms of the analogue of the theorem of the above mentioned work, and we find necessary and sufficient conditions for a kind of strengthening of this statement to be true.     

Ergodic sequences in the Fourier-Stieltjes algebra and measure algebra of a locally compact group

Let be a locally compact group. Blum and Eisenberg proved that if is abelian, then a sequence of probability measures on is strongly ergodic if and only if the sequence converges weakly to the Haar measure on the Bohr compactification of In this paper, we shall prove an extension of Blum and Eisenberg's Theorem for ergodic sequences in the Fourier-Stieltjes algebra of We shall also give an improvement to Milnes and Paterson's more recent generalization of Blum and Eisenberg's result to general locally compact groups, and we answer a question of theirs on the existence of strongly (or weakly) ergodic sequences of measures on

     

A Hadamard matrix of order 428

Four Turyn type sequences of lengths 36, 36, 36, 35 are found by a computer search. These sequences give new base sequences of lengths 71, 71, 36, 36 and are used to generate a number of new T‐sequences. The first order of many new Hadamard matrices constructible using these new T‐sequences is 428. © 2004 Wiley Periodicals, Inc.     

Cyclic BSEC of block size 3

Balanced sampling plans excluding contiguous units (or BSEC) were first introduced by Hedayat, Rao and Stufken in 1988. In this note, we discuss constructions of these designs having cyclic automorphisms. We use Langford sequences to construct all possible cyclic BSEC (or CBSEC) with block size 3 and λ = 1,2, which establishes the necessary and sufficient conditions for such designs. Some constructions of the balanced sampling plan avoiding adjacent units, a generalization of BSEC, are also given for fixed λ.     

任意随机变量序列级数的强收敛性

利用鞅差序列级数的收敛定理和条件三级数定理研究了任意随机变量序列级数的强收敛性,推广了某些经典的鞅差序列和独立随机变量序列及两两NQD序列的强极限定理.     

二阶矩限制下的Hajek-Renyi型不等式及其应用

在二阶矩限制下,获得了Hajek-Renyi型不等式,并给出了结果在PA,NA,Lr-混合序列场合下的应用.推广了Prakasa Rao关于PA序列的结果.     

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In this paper, by using central limit theorem of ND sequences and probability inequality, the precise asymptotics for partial sums of nonstationary ND sequences is investigated, and the same results with it under that of NA sequences are obtained.     

Parity Encoding of Binary Sequences

The parity encoding of binary sequences, which is essentially the inverse operation to the differentiationof binary sequences, partitions the sequences into cycles of sequences. The spectrum of these cycles is shown tobe a fractal-like semi-infinite sequence of powers of 2, with the property that truncating it at the(n + 1)st term yields the cycle spectrum for the parity encoding of the n-bitbinary sequences. A simple and complete characterization of both the cycles and of the cycle spectrum isgiven.