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Peter Borg 《Journal of Combinatorial Theory, Series A》2010,117(4):483-487
For positive integers r and n with r?n, let Pr,n be the family of all sets {(1,y1),(2,y2),…,(r,yr)} such that y1,y2,…,yr are distinct elements of [n]={1,2,…,n}. Pn,n describes permutations of [n]. For r<n, Pr,n describes permutations of r-element subsets of [n]. Families A1,A2,…,Ak of sets are said to be cross-intersecting if, for any distinct i and j in [k], any set in Ai intersects any set in Aj. For any r, n and k?2, we determine the cases in which the sum of sizes of cross-intersecting sub-families A1,A2,…,Ak of Pr,n is a maximum, hence solving a recent conjecture (suggested by the author). 相似文献
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Peter Borg 《Journal of Combinatorial Theory, Series A》2012,119(4):871-881
Families A1,A2,…,Ak of sets are said to be cross-intersecting if for any i and j in {1,2,…,k} with i≠j, any set in Ai intersects any set in Aj. For a finite set X, let X2 denote the power set of X (the family of all subsets of X). A family H is said to be hereditary if all subsets of any set in H are in H; so H is hereditary if and only if it is a union of power sets. We conjecture that for any non-empty hereditary sub-family H≠{∅} of X2 and any k?|X|+1, both the sum and the product of sizes of k cross-intersecting sub-families A1,A2,…,Ak (not necessarily distinct or non-empty) of H are maxima if A1=A2=?=Ak=S for some largest starSofH (a sub-family of H whose sets have a common element). We prove this for the case when H is compressed with respect to an element x of X, and for this purpose we establish new properties of the usual compression operation. As we will show, for the sum, the condition k?|X|+1 is sharp. However, for the product, we actually conjecture that the configuration A1=A2=?=Ak=S is optimal for any hereditary H and any k?2, and we prove this for a special case. 相似文献
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David Ellis 《Journal of Combinatorial Theory, Series A》2012,119(4):825-849
A family of permutations A⊂Sn is said to be t-set-intersecting if for any two permutations σ,π∈A, there exists a t-set x whose image is the same under both permutations, i.e. σ(x)=π(x). We prove that if n is sufficiently large depending on t, the maximum-sized t-set-intersecting families of permutations in Sn are cosets of stabilizers of t-sets. The t=2 case of this was conjectured by János Körner. It can be seen as a variant of the Deza-Frankl conjecture, proved in Ellis, Friedgut and Pilpel (2011) [3]. Our proof uses similar techniques to those of Ellis, Friedgut and Pilpel (2011) [3], namely, eigenvalue methods, together with the representation theory of the symmetric group, but the combinatorial part of the proof is harder. 相似文献
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A. A. Martynyuk 《Applicable analysis》2013,92(4):828-842
In this paper, for a family of impulsive equations, a heterogeneous matrix-valued Lyapunov-like function is considered, the comparison principle is formulated, and stability conditions for the set of stationary solutions are established. In addition, for a class of impulsive equations with uncertain parameters the monotone iterative technique for constructing a set of solutions is adapted. 相似文献
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WU SHIQUAN 《高校应用数学学报(英文版)》1994,9(2):149-152
SOLUTIONOFARESEARCHPROBLEMONTREESOFSUBSETS WUSHIQUANAbstract:Inthispaper,wesolvearesearchproblemontreesofsubsetsposedbyF.R.Mc?.. 相似文献
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M. Z. Garaev 《Proceedings of the American Mathematical Society》2008,136(8):2735-2739
Let be the field of prime order It is known that for any integer one can construct a subset with such that One of the results of the present paper implies that if with then
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We consider envelopes of one-parameter families of frontals in hyperbolic and de Sitter 2-space from the viewpoint of duality, respectively. Since the classical notions of envelopes for singular curves do not work, we have to find a new method to define the envelope for singular curves in hyperbolic space or de Sitter space. To do that, we first introduce notions of one-parameter families of Legendrian curves by using the Legendrian dualities. Afterwards, we give definitions of envelopes for the one-parameter families of frontals in hyperbolic and de Sitter 2-space, respectively. We investigate properties of the envelopes. At last, we give relationships among those envelopes. 相似文献
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In this paper, the concept of a family of L-fuzzy pseudo-norms on vector spaces is proposed and the characterization of L-vector topologies in terms of a family of L-fuzzy pseudo-norms is presented. As applications of the characterization, the Hausdorff separation property, convergence of molecule nets and boundedness of L-sets in L-topological vector spaces are investigated. 相似文献
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Laman's characterization of minimally rigid 2‐dimensional generic frameworks gives a matroid structure on the edge set of the underlying graph, as was first pointed out and exploited by L. Lovász and Y. Yemini. Global rigidity has only recently been characterized by a combination of two results due to T. Jordán and the first named author, and R. Connelly, respectively. We use these characterizations to investigate how graph theoretic properties such as transitivity, connectivity and regularity influence (2‐dimensional generic) rigidity and global rigidity and apply some of these results to reveal rigidity properties of random graphs. In particular, we characterize the globally rigid vertex transitive graphs, and show that a random d‐regular graph is asymptotically almost surely globally rigid for all d ≥ 4. © 2006 Wiley Periodicals, Inc. J Graph Theory 54: 154–166, 2007 相似文献
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Combinatorial ‐designs have wide applications in coding theory, cryptography, communications, and statistics. It is well known that the supports of all codewords with a fixed weight in a code may give a ‐design. In this paper, we first determine the weight distributions of a class of linear codes derived from the dual of some extended cyclic codes. We then obtain infinite families of 2‐designs and explicitly compute their parameters from the supports of all the codewords with a fixed weight in the codes. By a simple counting argument, we obtain exponentially many 2‐designs. 相似文献
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D. A. Tusupov 《Algebra and Logic》2007,46(4):281-286
The paper deals in questions on the complexity of isomorphisms and relations on universes of structures, on the number and
properties of numberings in various hierarchies of sets, and on the existence of connections between semantic and syntactic
properties of the structures and relations for the class of nilpotent groups of class two.
Supported by the Council for Grants (under RF President) and State Aid of Fundamental Science Schools via project NSh-4413.2006.1.
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Translated from Algebra i Logika, Vol. 46, No. 4, pp. 514–524, July–August, 2007. 相似文献
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In this paper, we establish the existence of some infinite families of 2‐designs from ‐dimensional projective geometry , which admit ‐dimensional projective special linear group as their flag‐transitive automorphism group. 相似文献