Báo cáo toán học: "Skolem-type Diﬀerence Sets for Cycle Systems)" pot

Báo cáo toán học: "On M-spectral sets and rationally invariant subspaces " pptx

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Báo cáo toán học: "Borel maps on sets of von Neumann algebras " pdf

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Báo cáo toán học: "On Eﬃcient Sets in R" potx

... differentif the ordering cone C is not pointed. So one must be careful when applyingresults in [4] for efficient points in the sense of (1) (as done in [2, p. 291]). Forinstance, Corollary 3.11 ... is efficient w.r.t. C in the sense of (2), while A has no efficient point w.r.t. C in the sense of (1).The set of efficient points of A w.r.t. C is called efficient set and denoted byE(A|C).If the interior ... optimal solution set, thenC is the intersection of On Efficient Sets in R2465m halfspaces, which contains a line and is therefore not pointed, as long asm<n. For instance, consider for the special...

Báo cáo toán học: "Improved LP Lower Bounds for Diﬀerence Triangle Sets" potx

... bounds and the bestupper bounds known. For example the lower bound for M(15, 10) in [1] is 958, the lower bound using Lorentzen and Nilsen’s formulation is 962 and the lower bound in this paperis ... programming to prove lower bounds on the size of diﬀerence triangle sets. In this note we show how to improvethese bounds by including additional valid linear inequalities in the LP formulation. Wealso ... linear programming (LP) methods to prove lower bounds on M(I,J). This was a generalization and improvement of earlier lower bounds. Here we show how to improve the LP bound (for I>1) by adding...

Báo cáo toán học: "Evolutionary Families of Sets" potx

... S of subsets of a finite set S whose union is S is connected if andonly if there is an evolutionary path in S between any two members of S.Proof:IfS is a finite connected family of subsets of ... themembers of iS[S] account for at least five of the seven nonempty subsets of S. Without losinggenerality we may assume that the complement in P(S) − {∅} of iS[S] is a subset of one of the following:(a) ... single member of S.Ifa(unique) member of S is of cardinality 1, then its unique element is considered to be a distin-guished vertex of G. The connectedness of S implies that of G. The family...

Báo cáo toán học: "Short Score Certiﬁcates for Upset Tournaments." potx

... (v2+p1+p2+···+pj,v2+p1+p2+···+pj+pj+1)forj=0,1,2, ,k−1. Note that upset arcs of an upset tournament form a path,which we call its upset path.An upset tournament T with vertices v1, ,vnis in standard form pro-vided ... T= T , and thus α ∪ β is a score certiﬁcate for T .Later we will show that the bound in Theorem 2.2 is not sharp in general.The construction of score certiﬁcates for upset tournaments given in ... (vi,vj)isinT’s upset path. Thus, each Tλis in standard form, and each upset tournament can beput into standard form by relabelling its vertices.Pictorially, each upset tournament, T , in standard form...

Báo cáo toán học: "Minimum connected dominating sets of random cubic graphs" docx

... theorem.Theorem 1 The size of a minimum connected dominating set of a random n-vertex cubic graph is asymptotically almost surely less than 0.5854n.Proof After the ﬁrst element of C has been chosen, ... least to within an additiveconstant, of the main result of [10]. They also showed that the size of a connected dominating set of an n-vertex cubic graph of girth at least 5 is at most 2n/3+O(1). ... reader is referred to [8].The algorithms of [4, 7], that ﬁnd a small connected dominating set of cubic graphs,guarantee that the size of the connected dominating set returned is at most 3n/4+O(1)in...

Báo cáo toán học: "Skolem-type Diﬀerence Sets for Cycle Systems)" pot

... +1|2mt+1=mt, the difference m-tuples obtained from a hooked Skolem-type m -cycle difference set oforder t form a modulo v difference set that uses edges of lengths 1, 2, ,mt.Theorem 3.3 For all integers ... Skolem-type m -cycle difference set of size t. Hence it remains to construct a Skolem-type m -cycle difference set of size t whenever mt ≡ 0, 3(mod 4) and a hooked Skolem-type m -cycle difference setof ... Skolem-type and hooked Skolem-type m -cycle difference sets of size t for all m ≥ 3andallt ≥ 1 (see Theorem 2.3). As a corollary, we obtain several existenceresults on cyclic m -cycle systems. These include...

Báo cáo toán học: "Spin-preserving Knuth correspondences for ribbon tableaux" potx

... there is an r -ribbon ofone of the given forms with its head on diagonal dk, with an increase of the sum for ribbons of the form à/, and a decrease of the sum for ribbons of the form /à;ineither ... that these Knuth correspondences are not derived from Schensted correspondences by means ofstandardisation. That method does not work for general r -ribbon tableaux, since for r ≥ 3, no r -ribbon ... 2r−1diﬀerent forms of r-ribbons.If () can be transformed into (à) by the replacement of a substring 1x0by0x1with x ∈{0, 1}r−1,thenx describes the form of the r -ribbon à/ by telling for eachfollowing...

Báo cáo toán học: "How diﬀerent can two intersecting families be" ppsx

... should be intersecting, weget that F should be intersecting and co -intersecting. So we conclude the followingClaim 3.3. max{D(F, G):F, G are intersecting} =max{ρ(F):F is intersecting and co -intersecting} . ... hypergraphs, and clearlyD(F, G) can t decrease.Case BF = ∅. (or similarlyG = ∅)the electronic journal of combinatorics 12 (2005), #R24 2 How different can two intersecting families be?Balázs PatkósDepartment ... differencebetween two intersecting set systems F, G⊆2[n]. If for any F ∈Fand G ∈Gwe haveF ∩ G = ∅,thenF∪Gis still an intersecting system of sets, so F and G are not really different as they are subfamilies...

Báo cáo toán học: "On small dense sets in Galois planes" pptx

... saturating sets in small projective geome-tries, European J. Combin. 21 (2000), 563–570.[7] A.A. Davydov, S. Marcugini and F. Pambianco, On saturating sets in projectivespaces, J. Combin. Theory ... As well as being a natural geometricalproblem, the construction of small dense sets in P G(2, q) is relevant in other areas ofCombinatorics, as dense sets are related to covering codes, see ... Proposition 2.5, the following result is obtained.Proposition 3.1. Let α1, α2be distinct elements in Fq. Then a point P = (u : v : 1)belongs to a line joining two points of DH,α1∪DH,α2provided...

Báo cáo toán học: "Totally Greedy Coin Sets and Greedy Obstructions" pptx

... coin sets. Finally, we ask about the asymptotics of the density of the set of totally greedy coin sets within the set of greedy coin sets. If G(k, R) denotes the set of all greedy coin sets with ... easyto test if a coin set is totally greedy. We begin to explore the theory of greedy obstructions– those coin sets that cannot be extended to greedy coin sets by theaddition of coins in larger ... ai) is greedy. That is, not only is the coin set greedy, but each initial segment of the coin set is also(totally) greedy. Lemma 1.5 There are greedy coin sets that are not totally greedy. the...

Báo cáo toán học: "Certiﬁcates of factorisation for chromatic polynomials" pot

... 1: Numbers of chromatic polynomials of degree at most 10. (A) Total number of chromatic polynomials, (B) number of chromatic polynomials of clique-separable g r aphsand (C) number of chromatic ... 4705Table 2: Chromatic factorisations of chromatic polynomials of degree n ≤ 10 of stronglynon-clique-separable graph.4 Certificates of Factorisation Definition A certificate o f factorisation of P(G, ... Number of steps s (s) in certificates of (extended) factorisation for chromatic polynomials of 8- and 9 -vertex strongly non-clique-separable graphs. For each certificatethe number of chromatic...

Báo cáo toán học: "The quantiﬁer semigroup for bipartite graph" pot

... y: w ≤ w′if wS ⊆ w′S for all G a nd all S ⊆ U.The focus of this paper is the partial order on the following semigroup: Definition 2. The quantifier semigroup for bipartite graphs, S, is defined ... can easily identifythe electronic journal of combinatorics 18 (2011), #P123 7 The quantifier semigroup for bipartite graphsLeonard J. Schulman∗Submitted: Jun 22, 2010; Accepted: May 17, 2011; ... h(w[ℓ) for all ℓ, o r there exists a J > j such that for all < J, h(w[J) < h(w[) y.ã y is a suffix valley if there exists a j such that h(w[j) = y, and either y ≤ h(w[ℓ) for all...

Báo cáo toán học: "A Diﬀerential Approach for Bounding the Index of Graphs under Perturbations" ppsx

... Addition of an edge The second result that we present is on the change of the index when we add an edge toa graph. In this context, Rowlinson [9] proved that, under some conditions, the index of the ... of interest. First,they are derived from a mere knowledge of the degrees of the vertices involved in the perturbation. Second, they are the best possible, in the sense that we characterize the cases ... complex plane. The spectral radius is the maximum of the modulus of its eigenvalues. If the matrix is the adjacency matrix of a graph, we call it the index of the graph. A symmetric real matrixhas...

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