Báo cáo toán học: "On identifying codes in the king grid that are robust against edge deletions" potx
Báo cáo hóa học: "ON EXTRAPOLATION BLOWUPS IN THE L p SCALE" docx
... several imbeddings. As observed earlier at the moment thereis no complete imbedding picture available for all the spaces involved. Two papers should 10 On extrapolation blowups in the L p scalebe ... Spaces, then the inclusion X⊂ Y implies the imbedding X Y (cf.,e.g., [1]). This particularly applies to al l the spaces in the following—they are al l BanachFunction Spaces.Some special ... Lorentz-Zygmund spaces the relations (1.4)readL p, p;βθ /p ⊂(sL) p, θ⊂ L p, p;θ /p .With help of Stirling’s formula it is not difficult to establish the following estimate for the norms in L 1(logL)γ(see,...
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Báo cáo toán học: "On point interactions in one dimension " pps
... alt ="" ...
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Báo cáo toán học: " On Score Sets in Tournaments" pptx
... Yao, Reid’s conjecture on score sets in tournaments, Kexue Tongbao 33(1988) 481–484 (in Chinese).7. T. X. Yao, On Reid’s conjecture of score sets for tournaments, Chinese Sci. Bull.34 (1989) ... of Reid’s conjecture by pure arithmeticalanalysis which appeared in Chinese [6] in 1988 and in English [7] in 1989. In the following result, we prove that any set of p non-negative integerss1,s2, ... Landau, On dominance relations and the structure of animal societies, III,the condition for a score structure, Bull. Math. Biophys. 15 (1953) 143–148.3. J. W. Moon, Topics on Tournaments Halt, Rinehart...
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Báo cáo toán học: "On Kissing Numbers in Dimensions 32 to 128" pptx
... 07 932- 0971, USASubmitted: April 9, 1998; Accepted: April 13, 1998ABSTRACTAn elementary construction using binary codes gives new record kissing numbers in dimensions from 32 to 128.1. IntroductionLet ... 1,260,230,400 in dimensions 32, 64 and 128, for example). In contrast, Quebbemann’s lattice Q 32 [14], [5, Chap. 8] has τ = 261,120. In recent years the kissing numbers of a few other lattices in dimensions ... kissing numbers of the best lattices known. On Kissing Numbers in Dimensions 32 to 128Yves EdelMathematisches Institut der UniversităatIm Neuenheimer Feld 28869120 Heidelberg, GermanyE. M. Rains...
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Báo cáo toán học: "On Catalan Trees and the Jacobian Conjecture" pdf
... standard(C) and the set of standardmarked Catalan trees by standard(C, ∗). The standard trees in C4are, , , , .One of the standard trees in CH3is. The standard tree representing the class [T ... those trees which are largest in their equivalence class asstandard trees, and use them as equivalence class representatives. We will de-note the set of standard Catalan trees by standard(C) and ... paper.2 Catalan Tree Expansion of the Inverse Catalan trees are rooted planar trees whose internal vertices have out-degree≥ 2. We will denote the set of Catalan trees by C and the set of Catalan trees...
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Báo cáo toán học: "Bent Hamilton Cycles in d-Dimensional Grid Graphs" pdf
... the dimensionof joining. Then P must contain w disjoint bent cycles that partition the vertices of P .Each of these w cycles must contain a wrapped edge in P along the joining dimension.Further, ... we join the endpoints with red arrows pointing away from each other to createthe new wrapped edges in G + P . We thus obtain a bent Hamilton cycle in Q(5, 3, 3),and by repeatedly joining ... edge going from this endpoint tothe corresponding endpoint in level i − 1. Similarly, if an endpoint in level i has nosurrounding circle then there is an edge going from such an endpoint to...
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Báo cáo toán học: "Fans and Bundles in the Graph of Pairwise Sums and Product" potx
... large integers .Theorem3.1. The graph Gì+contains -bundles for arbitrarily large integers .Inpar-ticular, for any positive integer , the graph Gì+contains subgraphs of the following type:nn1SSSSSSSSSSSSSSSSSSSSSSSSkkkkkkkkkkkkkkkkkkkkkkkkkkn2MMMMMMMMMMMMMMMMMppppppppppppppppppn3???????????~~~~~~~~~~~ ... 16 :(16, 48) ơy ; the electronic journal of combinatorics 11 (2004), #R6 10 Fans and Bundles in the Graph of Pairwise Sums and ProductsLorenz HalbeisenDepartment of Pure MathematicsQueen’s ... ơz ; and thus, we get a contradiction at 15. Finally, let us also consider the subgraphGì+ of Gì+dened as follows: The vertex-set of Gì+is again the set of positive integers, and...
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Báo cáo toán học: "On regular factors in regular graphs with small radius" ppsx
... edge-disjoint one factors and theexistence of k -factors in complete multipartite graphs, Discrete Math. 160 (1996)177–187.[5] T. Niessen and B. Randerath, Regular factors of simple regular graphs ... Theorems,Jahresber. Deutsch. Math Verein. 97 (1995) 19–42.the electronic journal of combinatorics 11 (2004), #R7 7 On regular factors in regular graphs with small radiusArne HoffmannLehrstuhl ... Theorie der regulăaren graphs, Acta Math. 15 (1891) 193–220.[7] W.T. Tutte, The factors of graphs, Canad. J. Math. 4 (1952) 314–328.[8] L. Volkmann, Regular graphs, regular factors, and the impact...
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Báo cáo toán học: "On Directed Triangles in Digraphs" pps
... theresulting digraph Dis acyclic.If true, this conjecture would imply the following strengthening of Lemma 5: Eachdigraph D obtained from a tournament by deleting k edges, that has no directed triangles, has ... with minimum outdegree atleast αn has a directed 3-cycle.Theorem 3. If β ≥ 0.34564, then each n-vertex digraph D in which both minimumoutdegree and minimum indegree is at least βn has a directed ... Seymour, Directed triangles in directed graphs, Discrete Math., 110 (1992), 279–282.the electronic journal of combinatorics 14 (2007), #N19 8 Then Bondy [1] relaxed the restriction on α in Theorem...
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Báo cáo toán học: "On identifying codes in the king grid that are robust against edge deletions" potx
... is r -identifying in all graphs G that can be obtained from G by deleting at mostt edges, we say that C is robust against t known edge deletions. Codes that are robust against t unknown edge ... to study codes that remain identifying, for instance, whensome edges are deleted in the underlying graph. In this paper we consider the followingtwo classes of robust identifying codes from ... Known edge deletions In this section we concentrate on the other class of robust identifying codes, namely, on the ones that are robust against known edge deletions.3.1 The case t ≥ 6There are...
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Báo cáo toán học: "On Mixed Codes with Covering Radius 1 and Minimum Distance 2" pot
... combinatorics 14 (2007), #R 51 10 Table II. Bounds on K(r, s, s; 2) for r ≤ 16 and 9 ≤ s ≤ 16 .s = 9 s = 10 s = 11 s = 12 s = 13 s = 14 s = 15 s = 16 r = 1 9 10 11 12 13 14 15 16 r = 2 16 B 18 B 20B ... 71F 72F a85E a96 − 98E a103 − 11 3E 11 0 − 12 6Gr = 13 60 − 65C 66 − 72C 73 − 81F 79 − 84C 85F a98E 10 5 − 11 3E a 117 − 12 8Er = 14 63 − 67C 70 − 76C 77 − 89F 84 − 92C 91 − 97F 98F a 113 E a126 − 12 8Er ... a 113 E a126 − 12 8Er = 15 69 − 73E 76C 84 − 95E 91 − 96C 99 − 10 9F 10 6 − 11 2C 11 3F a128Er = 16 b73H 80 − 84C 88 − 95C 96 − 10 4C 10 4 − 11 9F 11 2 − 12 2C 12 0 − 12 7F 12 8FReferences [1] Blokhuis, A. /...
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Báo cáo toán học: "On unimodality problems in Pascal’s triangle" potx
... decreasing (resp. increasing), and so the log-concavity impliesthe unimodality. The unimodality problems, including concavity (convexity) and log-concavity (log-convexity), arise naturally in many ... combinatorial interpretation. Latticepath techniques have been shown to be useful in solving the unimodality problem. As anexample, we present a combinatorial proof of Theorem 1 (ii) following ... precisely in one ofd − 2 open intervalskd,k+1d, where k = 1, . . . , d − 2. Indeed, neither two terms ofjδδ−1j=1nor two terms ofjd−δd−δ−1j=1are in the same interval since...
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Báo cáo toán học: "On winning fast in Avoider-Enforcer games" pps
... T. Szab´o, Fast winning strategies in Avoider-Enforcer games, Graphs Combin., 25 (2009), 533–544.[7] D. Hefetz, M. Krivelevich, M. Stojakovi´c and T. Szab´o, Fast winning strategies in Maker-Breaker ... laterHefetz et al. [7] studied the fast winning in Maker-Breaker Hamiltonicity game.We would like to emphasize that, generally speaking, results on fast winning in po-sitional games have an impact ... game F, we can make the set of hyperedges an increasing fa mily bythe electronic journal of combinatorics 17 (2010), #R56 2 On winning fast in Avoider-Enforcer gamesJ´anos Bar´at∗Department...
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Báo cáo toán học: "On some densities in the set of permutations" ppsx
... m) ≍ log m. Here and in the sequel the symbol a ≍ b means a ≪ b and b ≪ a while the electronic journal of combinatorics 17 (2010), #R100 6 On some densities in the set of permutationsEugenijus ... nontrivial outside the region of classical large deviations.Further, we apply them by inserting into the equalities given in Proposition 1. The veryidea goes back to the number-theoretical paper ... hidden in the second one. Instead of goinginto the details of that, we return to the cycle lengths and exploit Proposition 1. Set dk(m) = djk(σ) = m= (1 − e−1/m)Pm−1(k −1). (9)Theorem...
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