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1.
Necessary and sufficient conditions for the extendability of residual designs of Steiner systems S(t,t + 1,v) are studied. In particular, it is shown that a residual design with respect to a single point is uniquely extendable, and the extendability of a residual design with respect to a pair of points is equivalent to a bipartition of the block graph of a related design. © 1993 John Wiley & Sons, Inc. 相似文献
2.
A k-dimensional box is a Cartesian product R
1 × · · · × R
k
where each R
i
is a closed interval on the real line. The boxicity of a graph G, denoted as box(G), is the minimum integer k such that G can be represented as the intersection graph of a collection of k-dimensional boxes. That is, two vertices are adjacent if and only if their corresponding boxes intersect. A circular arc
graph is a graph that can be represented as the intersection graph of arcs on a circle. We show that if G is a circular arc graph which admits a circular arc representation in which no arc has length at least
p(\fraca-1a){\pi(\frac{\alpha-1}{\alpha})} for some
a ? \mathbbN 3 2{\alpha\in\mathbb{N}_{\geq 2}}, then box(G) ≤ α (Here the arcs are considered with respect to a unit circle). From this result we show that if G has maximum degree
D < ?\fracn(a-1)2a?{\Delta < \lfloor{\frac{n(\alpha-1)}{2\alpha}}\rfloor} for some
a ? \mathbbN 3 2{\alpha \in \mathbb{N}_{\geq 2}}, then box(G) ≤ α. We also demonstrate a graph having box(G) > α but with
D = n\frac(a-1)2a+ \fracn2a(a+1)+(a+2){\Delta=n\frac{(\alpha-1)}{2\alpha}+ \frac{n}{2\alpha(\alpha+1)}+(\alpha+2)}. For a proper circular arc graph G, we show that if
D < ?\fracn(a-1)a?{\Delta < \lfloor{\frac{n(\alpha-1)}{\alpha}}\rfloor} for some
a ? \mathbbN 3 2{\alpha\in \mathbb{N}_{\geq 2}}, then box(G) ≤ α. Let r be the cardinality of the minimum overlap set, i.e. the minimum number of arcs passing through any point on the circle, with
respect to some circular arc representation of G. We show that for any circular arc graph G, box(G) ≤ r + 1 and this bound is tight. We show that if G admits a circular arc representation in which no family of k ≤ 3 arcs covers the circle, then box(G) ≤ 3 and if G admits a circular arc representation in which no family of k ≤ 4 arcs covers the circle, then box(G) ≤ 2. We also show that both these bounds are tight. 相似文献
3.
Sanpei Kageyama 《Annals of the Institute of Statistical Mathematics》1987,39(1):661-669
Summary This paper investigates locally resistant balanced incomplete block (LRBIB) designs of degree one. A new necessary condition
for the existence of such an LRBIB design is presented. This condition yields a complete characterization of affine α-resolvable
LRBIB designs of degree one. Furthermore, regarding construction methods of LRBIB designs of degree one, it is shown that
Shah and Gujarathi's method (1977,Sankhy?, B39, 406–408) yields the same parameters as Hedayat and John's method (1974,Ann. Statist.,2, 148–158), but their block structures are different and interesting.
Partially supported by Grants 59540043 (C) and 60530014 (C). 相似文献
4.
Yutaka Hiramine 《Designs, Codes and Cryptography》2011,60(1):91-99
Many classes of symmetric transversal designs have been constructed from generalized Hadamard matrices and they are necessarily
class regular. In (Hiramine, Des Codes Cryptogr 56:21–33, 2010) we constructed symmetric transversal designs using spreads
of
\mathbbZp2n{\mathbb{Z}_p^{2n}} with p a prime. In this article we show that most of them admit no class regular automorphism groups. This implies that they are
never obtained from generalized Hadamard matrices. As far as we know, this is the first infinite family of non class-regular
symmetric transversal designs. 相似文献
5.
Éric Marchand François Perron 《Annals of the Institute of Statistical Mathematics》2009,61(1):215-234
For the problem of estimating under squared error loss the parameter of a symmetric distribution which is subject to an interval
constraint, we develop general theory which provides improvements on various types of inadmissible procedures, such as maximum
likelihood procedures. The applications and further developments given include: (i) symmetric location families such as the
exponential power family including double-exponential and normal, Student and Cauchy, a Logistic type family, and scale mixture
of normals in cases where the variance is lower bounded; (ii) symmetric exponential families such as those related to a Binomial(n,p) model with bounded |p−1/2| and to a Beta(α + θ, α −θ) model; and (iii) symmetric location distributions truncated to an interval (−c,c). Finally, several of the dominance results are studied with respect to model departures yielding robustness results, and
specific findings are given for scale mixture of normals and truncated distributions.
Research supported by NSERC of Canada. 相似文献
6.
John Arhin 《Designs, Codes and Cryptography》2007,43(2-3):103-114
We introduce the notion of an unrefinable decomposition of a 1-design with at most two block intersection numbers, which is
a certain decomposition of the 1-designs collection of blocks into other 1-designs. We discover an infinite family of 1-designs
with at most two block intersection numbers that each have a unique unrefinable decomposition, and we give a polynomial-time
algorithm to compute an unrefinable decomposition for each such design from the family. Combinatorial designs from this family
include: finite projective planes of order n; SOMAs, and more generally, partial linear spaces of order (s, t) on (s + 1)2 points; as well as affine designs, and more generally, strongly resolvable designs with no repeated blocks.
相似文献
7.
An H-design is said to be (1, α)-resolvable, if its block set can be partitioned into α-parallel classes, each of which contains every point of the design exactly α times. When α = 1, a (1, α)-resolvable H-design of type g
n
is simply called a resolvable H-design and denoted by RH(g
n
), for which the general existence problem has been determined leaving mainly the case of g ≡ 0 (mod 12) open. When α = 2, a (1, 2)-RH(1
n
) is usually called a (1, 2)-resolvable Steiner quadruple system of order n, for which the existence problem is far from complete. In this paper, we consider these two outstanding problems. First,
we prove that an RH(12
n
) exists for all n ≥ 4 with a small number of possible exceptions. Next, we give a near complete solution to the existence problem of (1, 2)-resolvable
H-designs with group size 2. As a consequence, we obtain a near complete solution to the above two open problems. 相似文献
8.
Kirsten Mackenzie-Fleming 《Journal of Geometry》2000,67(1-2):173-179
LetD be a quasi-residual Hadamard design with =(2m + 1)2n–1, wherem andn are positive integers. IfD contains a pair of blocks intersecting in m2n+1 points together with a third block intersecting each of the first two blocks in (m + 1)2n points thenD is non-embeddable. Using this result together with a recursive construction for quasi-residual Hadamard designs the existence of a previously unknown infinite family of non-embeddable quasi-residual Hadamard designs with =5(2n)–1 is established. An additional infinite family of non-embeddable quasi-residual Hadamard designs is given. This family has = 2n–1 with each design in the family having a pair of blocks meeting in (3 + 3)/4 points and a third block meeting each of the first two blocks in (5 + 5)/8 points. 相似文献
9.
Frank Pacard 《manuscripta mathematica》1993,79(1):161-172
For scalar non-linear elliptic equations, stationary solutions are defined to be critical points of a functional with respect
to the variations of the domain. We consideru a weak positive solution of −Δu=u
α in -Δu=u
α in Ω ⊂ ℝ
n
, which is stationary. We prove that the Hausdorff dimension of the singular set ofu is less thann−2α+1/α−1, if α≥n+2/n−2. 相似文献
10.
Quasi-symmetric designs are block designs with two block intersection numbersx andy It is shown that with the exception of (x, y)=(0, 1), for a fixed value of the block sizek, there are finitely many such designs. Some finiteness results on block graphs are derived. For a quasi-symmetric 3-design
with positivex andy, the intersection numbers are shown to be roots of a quadratic whose coefficients are polynomial functions ofv, k and λ. Using this quadratic, various characterizations of the Witt—Lüneburg design on 23 points are obtained. It is shown
that ifx=1, then a fixed value of λ determines at most finitely many such designs. 相似文献
11.
It is shown that quasi-symmetric designs which are derived or residual designs of nonisomorphic symmetric designs with the symmetric difference property are also nonisomorphic. Combined with a result by W. Kantor, this implies that the number of nonisomorphic quasi-symmetric designs with the symmetric difference property grows exponentially. The column spaces of the incidence matrices of these designs provide an exponential number of inequivalent codes meeting the Grey-Rankin bound. A transformation of quasi-symmetric designs by means of maximal arcs is described. In particular, a residual quasi-symmetric design with the symmetric difference property is transformed into a quasi-symmetric design with the same block graph but higher rank over GF(2).Dedicated to Professor Hanfried Lenz on the occasion of his 75th birthday.This paper was written while the author was at the University of Giessen as a Research Fellow of the Alexander von Humboldt Foundation, on leave from the University of Sofia, Bulgaria. 相似文献
12.
Themaximal minor polytope Π
m, n
is the Newton polytope of the product of all maximal minors of anm×n matrix of indeterminates. The family of polytopes {Π
m, n
} interpolates between the symmetric transportation polytope (form=n−1) and the permutohedron (form=2). Both transportation polytope and the permutohedron aresimple polytopes but in general Π
m, n
is not simple. The main result of this paper is an explicit construction of a class of simple vertices of Π
m, n
for generalm andn. We call themvertices of diagonal type. For every such vertexv we explicitly describe all the edges and facets of Π
m, n
which containv. Simple vertices of Π
m, n
have an interesting algebro-geometric application: they correspond tononsingular extreme toric degenerations of the determinantal variety ofm×n matrices not of full rank.
Andrei Zelevinsky was partially supported by the NSF under Grant DMS-9104867. 相似文献
13.
V. A. Ustimenko 《Journal of Mathematical Sciences》2007,140(3):461-471
The paper is devoted to the study of a linguistic dynamical system of dimension n ≥ 2 over an arbitrary commutative ring K,
i.e., a family F of nonlinear polynomial maps f
α : K
n
→ K
n
depending on “time” α ∈ {K − 0} such that f
α
−1 = f
−αM, the relation f
α1 (x) = f
α2 (x) for some x ∈ Kn implies α1 = α2, and each map f
α has no invariant points. The neighborhood {f
α (υ)∣α ∈ K − {0}} of an element v determines the graph Γ(F) of the dynamical system on the vertex set Kn. We refer to F as a linguistic dynamical system of rank d ≥ 1 if for each string a = (α1, υ, α2), s ≤ d, where αi + αi+1 is a nonzero divisor for i = 1, υ, d − 1, the vertices υ
a = f
α1 × ⋯ × f
αs
(υ) in the graph are connected by a unique path. For each commutative ring K and each even integer n ≠= 0 mod 3, there is a family of linguistic dynamical systems Ln(K) of rank d ≥ 1/3n. Let L(n, K) be the graph of the dynamical system Ln(q). If K = Fq, the graphs L(n, Fq) form a new family of graphs of large girth. The projective limit L(K) of L(n, K), n → ∞, is well defined for each commutative
ring K; in the case of an integral domain K, the graph L(K) is a forest. If K has zero divisors, then the girth of K drops
to 4. We introduce some other families of graphs of large girth related to the dynamical systems Ln(q) in the case of even q. The dynamical systems and related graphs can be used for the development of symmetric or asymmetric
cryptographic algorithms. These graphs allow us to establish the best known upper bounds on the minimal order of regular graphs
without cycles of length 4n, with odd n ≥ 3. Bibliography: 42 titles.
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 326, 2005, pp. 214–234. 相似文献
14.
If π is a set of primes, a finite group G is block π-separated if for every two distinct irreducible complex characters α, β ∈ Irr(G) there exists a prime p ∈ π such that α and β lie in different Brauer p-blocks. A group G is block separated if it is separated by the set of prime divisors of |G|. Given a set π with n different primes, we construct an example of a solvable π-group G which is block separated but it is not separated by every proper subset of π.
Received: 22 December 2004 相似文献
15.
Let f be an orientation-preserving circle homeomorphism and Φ the Douady-Earle extension of f. In this paper, we show that the quasiconformality and asymptotic conformality of Φ are local properties; i.e., if f is quasisymmetric or symmetric on an arc of the unit circle, then Φ is quasiconformal or asymptotically conformal nearby.
Furthermore, our methods enable us to conclude the global quasiconformality and asymptotic conformality from local properties.
In the quasiconformal case, our methods also enable us to provide an upper bound for the maximal dilatation of Φ on a neighborhood
of the arc in the open unit disk in terms of the cross-ratio distortion norm of f on the arc. 相似文献
16.
A defining set of a t-(v, k, λ) design is a partial design which is contained in a unique t-design with the given parameters. A minimal defining set is a defining set, none of whose proper partial designs is a defining
set. This paper proposes a new and more efficient algorithm that finds all non-isomorphic minimal defining sets of a given
t-design. The complete list of minimal defining sets of 2-(6, 3, 6) designs, 2-(7, 3, 4) designs, the full 2-(7, 3, 5) design,
a 2-(10, 4, 4) design, 2-(10, 5, 4) designs, 2-(13, 3, 1) designs, 2-(15, 3, 1) designs, the 2-(25, 5, 1) design, 3-(8, 4,
2) designs, the 3-(12, 6, 2) design, and 3-(16, 8, 3) designs are given to illustrate the efficiency of the algorithm. Also,
corrections to the literature are made for the minimal defining sets of four 2-(7, 3, 3) designs, two 2-(6, 3, 4) designs
and the 2-(21, 5, 1) design. Moreover, an infinite class of minimal defining sets for 2-((v) || 3){v\choose3} designs, where v ≥ 5, has been constructed which helped to show that the difference between the sizes of the largest and the smallest minimal
defining sets of 2-((v) || 3){v\choose3} designs gets arbitrarily large as v → ∞. Some results in the literature for the smallest defining sets of t-designs have been generalized to all minimal defining sets of these designs. We have also shown that all minimal defining
sets of t-(2n, n, λ) designs can be constructed from the minimal defining sets of their restrictions when t is odd and all t-(2n, n, λ) designs are self-complementary. This theorem can be applied to 3-(8, 4, 3) designs, 3-(8, 4, 4) designs and the full 3-(8 || 4)3-{8 \choose 4} design using the previous results on minimal defining sets of their restrictions. Furthermore we proved that when n is even all (n − 1)-(2n, n, λ) designs are self-complementary. 相似文献
17.
S. De Winter 《Journal of Algebraic Combinatorics》2006,24(3):285-297
Let be a proper partial geometry pg(s,t,2), and let G be an abelian group of automorphisms of acting regularly on the points of . Then either t≡2±od
s+1 or is a pg(5,5,2) isomorphic to the partial geometry of van Lint and Schrijver (Combinatorica 1 (1981), 63–73). This result is a new step towards the classification of partial geometries with an abelian Singer group and further provides an interesting characterization of the geometry of van Lint and Schrijver.The author is Postdoctoral Fellow of the Fund for Scientific Research Flanders (FWO-Vlaanderen). 相似文献
18.
We prove that every digraph D with n≥7, n≥+6 vertices and at least (n−k−1)(n−1)+k(k+1) arcs contains all symmetric cycles of length at most n−k−2, an almost symmetric cycle of length n−k−1, and with some exceptions, also an almost symmetric cycle of length n−k. Consequently, D contains all orientations of cycles of length at most n−k, unless D is an exception.
The research was partially supported by the AGH University of Science and Technology grant No 11 420 04 相似文献
19.
We present a new network simplex pivot selection rule, which we call theminimum ratio pivot rule, and analyze the worst-case complexity of the resulting network simplex algorithm. We consider networks withn nodes,m arcs, integral arc capacities and integral supplies/demands of nodes. We define a {0, 1}-valued penalty for each arc of the
network. The minimum ratio pivot rule is to select that eligible arc as the entering arc whose addition to the basis creates
a cycle with the minimum cost-to-penalty ratio. We show that the so-defined primal network simplex algorithm solves minimum
cost flow problem within O(nΔ) pivots and in O(Δ(m + n logn)) time, whereΔ is any upper bound on the sum of all arc flows in every feasible flow. For assignment and shortest path problems, our algorithm
runs in O(n
2) pivots and O(nm +n
2 logn) time. 相似文献
20.
We give two constructions of a balanced incomplete‐block design discovered by van Lint: the design has parameters (13,39,15,5,5), and has repeated blocks and an automorphism group of order 240. One of these methods can be generalized to produce a large class of designs with the properties of the title. © 2006 Wiley Periodicals, Inc. J Combin Designs 相似文献