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1.
R. Wei 《Discrete Mathematics》2002,250(1-3):291-298
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. 相似文献
2.
In this article, a kind of auxiliary design BSA* for constructing BSAs is introduced and studied. Two powerful recursive constructions on BSAs from 3‐IGDDs and BSA*s are exploited. Finally, the necessary and sufficient conditions for the existence of a BSA(v, 3, λ; α) with α = 2, 3 are established. © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 61–76, 2007 相似文献
3.
In this work we present a study of the Pearson discrete distributions generated by the hypergeometric function 3F2(α1, α2, α3;γ1, γ2; λ), a univariate extension of the Gaussian hypergeometric function, through a constructive methodology. We start from the polynomial coefficients of the difference equation that lead to such a function as a solution. Immediately after, we obtain the generating probability function and the differential equation that it satisfies, valid for any admissible values of the parameters. We also obtain the differential equations that satisfy the cumulants generating function, moments generating function and characteristic function, From this point on, we obtain a relation in recurrences between the moments about the origin, allowing us to create an equation system for estimating the parameters by the moment method. We also establish a classification of all possible distributions of such type and conclude with a summation theorem that allows us study some distributions belonging to this family. © 1997 by John Wiley & Sons, Ltd. 相似文献
4.
A group divisible design GD(k,λ,t;tu) is α‐resolvable if its blocks can be partitioned into classes such that each point of the design occurs in precisely α blocks in each class. The necessary conditions for the existence of such a design are λt(u ? 1) = r(k ? 1), bk = rtu, k|αtu and α|r. It is shown in this paper that these conditions are also sufficient when k = 3, with some definite exceptions. © 2004 Wiley Periodicals, Inc. 相似文献
5.
An m-cycle system of order ν and index λ, denoted by rn-CS(ν, λ), is a collection of cycles of length m whose edges partition the edges of λκ_v. An m-CS(ν, λ) is α-resolvable if its cycles can be partitioned into classes such that each point of the design occurs in precisely α cycles in each class. The necessary conditions for the existence of such a design are m|λν(ν-1)/2,2|λ(ν-1), m|αν,α|λ(ν-1)/2 It is shown in this paper that these conditions are also sufficient when m = 4. 相似文献
6.
Abstact: An α‐resolvable BIBD is a BIBD with the property that the blocks can be partitioned into disjoint classes such that every class contains each point of the design exactly α times. In this paper, we show that the necessary conditions for the existence of α‐resolvable designs with block size four are sufficient, with the exception of (α, ν, λ) = (2, 10, 2). © 2000 John Wiley & Sons, Inc. J Combin Designs 9: 1–16, 2001 相似文献
7.
We study the asymptotic, long-time behavior of the energy function where {Xs : 0 ≤ s < ∞} is the standard random walk on the d-dimensional lattice Zd, 1 < α ≤ 2, and f:R+ → R+ is any nondecreasing concave function. In the special case f(x) = x, our setting represents a lattice model for the study of transverse magnetization of spins diffusing in a homogeneous, α-stable, i.i.d., random, longitudinal field {λV(x) : x ∈ Zd} with common marginal distribution, the standard α-symmetric stable distribution; the parameter λ describes the intensity of the field. Using large-deviation techniques, we show that Sc(λ α f) = limt→∞ E(t; λ f) exists. Moreover, we obtain a variational formula for this decay rate Sc. Finally, we analyze the behavior Sc(λ α f) as λ → 0 when f(x) = xβ for all 1 ≥ β > 0. Consequently, several physical conjectures with respect to lattice models of transverse magnetization are resolved by setting β = 1 in our results. We show that Sc(λ, α, 1) ≈ λα for d ≥ 3, λagr;(ln 1/λ)α−1 in d = 2, and in d = 1. © 1996 John Wiley & Sons, Inc. 相似文献
8.
Marco Buratti 《组合设计杂志》2001,9(3):215-226
Phelps and Rosa introduced the concept of 1‐rotational Steiner triple system, that is an STS(ν) admitting an automorphism consisting of a fixed point and a single cycle of length ν ? 1 [Discrete Math. 33 ( 12 ), 57–66]. They proved that such an STS(ν) exists if and only if ν ≡ 3 or 9 (mod 24). Here, we speak of a 1‐rotational STS(ν) in a more general sense. An STS(ν) is 1‐rotational over a group G when it admits G as an automorphism group, fixing one point and acting regularly on the other points. Thus the STS(ν)'s by Phelps and Rosa are 1‐rotational over the cyclic group. We denote by ??1r, ??1r, ??1r, ??1r, the spectrum of values of ν for which there exists a 1‐rotational STS(ν) over an abelian, a cyclic, a dicyclic, and an arbitrary group, respectively. In this paper, we determine ??1r and find partial answers about ??1r and ??1r. The smallest 1‐rotational STSs have orders 9, 19, 25 and are unique up to isomorphism. In particular, the only 1‐rotational STS(25) is over SL2(3), the special linear group of dimension 2 over Z3. © 2001 John Wiley & Sons, Inc. J Combin Designs 9: 215–226, 2001 相似文献
9.
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. 相似文献
10.
Joseph Hershenov 《Studies in Applied Mathematics》1976,55(4):301-314
This paper deals with the solutions of the differential equation u?+λ2zu+(α?1)λ2u=0, in which λ is a complex parameter of large absolute value and α is an arbitrary constant, real or complex. After a discussion of the structure of the solutions of the differential equation, an integral representation of the solution is given, from which the series solutions and their asymptotic representations are derived. A third independent solution is needed for the special case when α?1 is a positive integer, and two derivations for this are given. Finally, a comparison is made with the results obtained by R. E. Langer. 相似文献
11.
In a (v, k, λ: w) incomplete block design (IBD) (or PBD [v, {k, w*}. λ]), the relation v ≥ (k ? 1)w + 1 must hold. In the case of equality, the IBD is referred to as a block design with a large hole, and the existence of such a configuration is equivalent to the existence of a λ-resolvable BIBD(v ? w, k ? 1, λ). The existence of such configurations is investigated for the case of k = 5. Necessary and sufficient conditions are given for all v and λ ? 2 (mod 4), and for λ ≡ 2 mod 4 with 11 possible exceptions for v. © 1993 John Wiley & Sons, Inc. 相似文献
12.
A pitch tournament is a resolvable or near resolvable(ν,8,7) BIBD that satisfies certain criteria in addition to theusual condition that ν ≡ 0 or 1 (mod 8). Here we establish that for the case ν = 8n the necessary condition forpitch tournaments is sufficient for all n > 1615, with at most 187 smaller exceptions. This complements our earlier study of the ν = 8n + 1 case, where we established sufficiency for all n > 224, with at most 28 smaller exceptions. The four missing cases for (ν,8,7) BIBDs are provided, namely ν∈{48,56,96,448}, thereby establishing that the necessary existence conditions are sufficient without exception. Some constructions for resolvable designs are also provided, reducing the existence question for (ν,8,7) RBIBDs to 21 possible exceptions. © 2001 John Wiley & Sons, Inc. J Combin Designs 9: 334–356, 2001 相似文献
13.
《Discrete Mathematics》2022,345(3):112719
We answer a question of Brown and Jordon (2021) [4] by proving the existence of signed Langford sequences of every possible order for each defect. Our proof is constructive, and the constructions are shown to have other interesting properties and connections to several conjectures concerning permutations and partial sums of sequences of elements from cyclic groups. 相似文献
14.
Ahmed M. Assaf 《组合设计杂志》1993,1(6):453-458
A (v, k. λ) covering design of order v, block size k, and index λ is a collection of k-element subsets, called blocks, of a set V such that every 2-subset of V occurs in at least λ blocks. The covering problem is to determine the minimum number of blocks, α(v, k, λ), in a covering design. It is well known that $ \alpha \left({\nu,\kappa,\lambda } \right) \ge \left\lceil {\frac{\nu}{\kappa}\left\lceil {\frac{{\nu - 1}}{{\kappa - 1}}\lambda} \right\rceil} \right\rceil = \phi \left({\nu,\kappa,\lambda} \right) $, where [χ] is the smallest integer satisfying χ ≤ χ. It is shown here that α (v, 5, λ) = ?(v, 5, λ) + ? where λ ≡ 0 (mod 4) and e= 1 if λ (v?1)≡ 0(mod 4) and λv (v?1)/4 ≡ ?1 (mod 5) and e= 0 otherwise With the possible exception of (v,λ) = (28, 4). © 1993 John Wiley & Sons, Inc. 相似文献
15.
Beiliang Du 《组合设计杂志》2004,12(6):404-420
Splitting balanced incomplete block designs were first formulated by Ogata, Kurosawa, Stinson, and Saido recently in the investigation of authentication codes. This article investigates the existence of splitting balanced incomplete block designs, i.e., (v, 3k, λ)‐splitting BIBDs; we give the spectrum of (v, 3 × 2, λ)‐splitting BIBDs. As an application, we obtain an infinite class of 2‐splitting A‐codes. © 2004 Wiley Periodicals, Inc. 相似文献
16.
Cunsheng Ding 《组合设计杂志》2008,16(2):164-171
In this article, two constructions of (v, (v ? 1)/2, (v ? 3)/2) difference families are presented. The first construction produces both cyclic and noncyclic difference families, while the second one gives only cyclic difference families. The parameters of the second construction are new. The difference families presented in this article can be used to construct Hadamard matrices. © 2007 Wiley Periodicals, Inc. J Combin Designs 16: 164–171, 2008 相似文献
17.
An affine α-resolvable PBD of index λ is a triple (V, B, R), where V is a set (of points), B is a collection of subsets of V (blocks), and R is a partition of B (resolution), satisfying the following conditions: (i) any two points occur together in λ blocks, (ii) any point occurs in α blocks of each resolution class, and (iii) |B| = |V| + |R| − 1. Those designs embeddable in symmetric designs are described and two infinite series of embeddable designs are constructed. The analog of the Bruck–Ryser–Chowla theorem for affine α-resolvable PBDs is obtained. © 1998 John Wiley & Sons, Inc. J Combin Designs 6:111–129, 1998 相似文献
18.
We classify all {δ (p3 + 1), δ; 3, p3}‐minihypers, , for a prime number p0 ≥ 7, with excess e ≤ p3. Such a minihyper is a sum of lines and of possibly one projected subgeometry PG(5, p), or a sum of lines and a minihyper which is a projected subgeometry PG(5, p) minus one line. When p is a square, also (possibly projected) Baer subgeometries PG(3, p3/2) can occur. © 2004 Wiley Periodicals, Inc. 相似文献
19.
Lu Qinglin 《组合设计杂志》1994,2(1):1-13
In this article, we investigate the existence of pure (v, 4, λ)-PMD with λ = 1 and 2, and obtain the following results: (1) a pure (v, 4, 1)-PMD exists for every positive integer v = 0 or 1 (mod 4) with the exception of v = 4 and 8 and the possible exception of v = 12; (2) a pure (v, 4, 2)-PMD exists for every integer v ≥ 6. © 1994 John Wiley & Sons, Inc. 相似文献
20.
Yanfang Zhang 《组合设计杂志》2005,13(6):462-465
Let G = (V(G),E(G)) be a graph. A (ν, G, λ)‐GD is a partition of all the edges of λKν into subgraphs (G‐blocks), each of which is isomorphic to G. The (ν, G, λ)‐GD is named as graph design for G or G‐decomposition. The large set of (ν, G, λ)‐GD is denoted by (ν, G, λ)‐LGD. In this paper, we obtain a general result by using the finite fields, that is, if q ≥ k ≥ 2 is an odd prime power, then there exists a (q,Pk, k ? 1)‐LGD. © 2005 Wiley Periodicals, Inc. J Combin Designs. 相似文献