Báo cáo toán học: " Lower Bounds on van der Waerden Numbers: Randomized- and Deterministic-Constructive" pdf

... combinatorics 18 (2011), #P64 5 Lower Bounds on van der Waerden Numbers: Randomized- and Deterministic-ConstructiveWillia m GasarchDepartment of Computer ScienceUniversity of Maryland at College ParkCollege ... called nonconstructive in contrast to constructive pr oofs that provide anefficient algorithm.This paper clarifies these notions and gives d efi nitions for deterministic- and randomized-constructive ... get lower bounds for variants of van der Waerden numbers such asGallai-Witt numbers (multi-dimensional va n der Warden Numbers) [20, 21] (see also[8, 10]), and some polynomial van der Waerden...

Báo cáo toán học: "A New Method to Construct Lower Bounds for Van der Waerden Numbers" pdf

... 132.2 Current bounds of Van der Waerden numbersOnly five smaller Van der Waerden numbers are known at present. The known Van der Waerden numbers, as well as the best known lower bounds and their ... ConclusionsIn this paper we presented a method to construct lower bounds for Van der Waerden numbers. The final results are shown in table 4.Table 4: Known Van der Waerden numbers and known and ... bounds, but also providescertificates for all the other proved and currently known lower bounds for Van der Waerden numbers with even r. The only exception is the lower bound of the Van der Waerden number...

Báo cáo toán học: "The Bounds on Components of the Solution for Consistent Linear Systems" pdf

... (1993) 1–8.4. W. Li, On the property of solutions ofM-matrix equations, Systems Science and Math. S cience 10 (1997) 129–132.The Bounds on Comp onents of the Solution for Consistent Linear Systems ... nucleus K of A on one hand. On the other hand, inTheorem 2.4 and Corollary 2.5 we need not to assume that A is nonsingular.Hence from the fact that each principal submatrix of a nonsingular M-matrixis ... Introduction and DeﬁnitionsIn [2, 3] the a uthors consider the following consistent linear systemAx = b, (1)where A is an n×nM-matrix, b is an n dimension vector in rang(A). The studyof the solution...

Báo cáo toán học: "Improved bounds on the length of maximal abelian square-free word" pot

... ˜w4˜w5˜w6˜w7,itmustbethat m = 3 and the subword to the left of the leftmost 6 in w contains two 0’s, two 1’s, and two 2’s. However, w1must consist of 0 and 1 in some order, and w2of 1 and 2, sothe two ... 1)’s in wm, one must be on the left half of sm and hence before the m in hm+1 ,and the other must be on the right half of sk−1 and hence after the k − 2inhk−1.It now remains only to show ... ﬁrst, being in w2andonthelefthalf of sk−1, would be in hk−1, and there would then be an additional pair of (k − 1)’s inwk−1, which is a contradiction.the electronic journal of combinatorics...

Báo cáo toán học: "Lower bounds for the football pool problem for 7 and 8 matches" pdf

... 1) and limit the degree of irregularity of its solutions (Lemma 2). In section 3 we start with somepreliminaries. Section 4 contains a proof of k3(7) ≥ 155. The more detailed considerationsneeded ... postponed to the next section. The reader interestedin this bound should keep track about some consequences of assumed equality in (13)throughout this and the previous section. These consequences ... (1111) and ρ3= (2222). Now consider σ = (2000). By L) there exists τ ∈ F43with d(ρ1, τ) = 2,d(σ, τ) = 1 and nτ≥ 3, say τ = (2100) (the case τ = (2200) is excluded by K)).Now consider...

Báo cáo toán học: "Lower Bounds for the Size of Random Maximal H-Free Graphs" pdf

... above lower bounds trivially imply similar lower bounds on the expectation ofe(Mn(H)). It is worth mentioning that all of the above lower bounds on the expectationof e(Mn(H)) can be derived ... Janson, T. Luczak, and A. Ruci´nski, Random graphs, 2000.[8] S. Janson, Poisson approximation for large deviations, Random Struct. Algorithms 1(1990), 221–230.[9] D. Osthus and A. Taraz, Random ... lemmas are provedin Sections 3 and 4 and these two sections correspond to the two parts of the proof thatwere sketched at Section 1.2.1.4 Basic notation and conventionsWe use Knto denote...

Báo cáo toán học: "Lower Bounds for q-ary Codes with Large Covering Radius" ppsx

... m for 1  i  q and player T chooses one of the sets. Then player P choosesa second partition with the sam e properties and again player T chooses one of the sets.This goes on until player ... and covering radius R.For a monograph on covering codes see [2]. An updated table of bounds on Kq(n, R)is published online by K´eri [5]. An easy lower bound on Kq(n, R) is the sphere-coveringboundKq(n, ... their(generalized) transversals and the connection to covering codes. In Section 3 we considerthe game from above a nd describe how to compute winning strategies for player T. Inthe electronic journal of combinatorics...

Báo cáo toán học: "Lower bounds for identifying codes in some inﬁnite grids" potx

... direction, we will only count the number of ones in rowscorresponding to vertices in Qm−r. There can be at most K of these rows that conta in asingle one and at most Pmof these rows which contain ... Daniel W. Cranston and Gexin Yu. A new lower bound on the density of vertexidentifying codes for the inﬁnite hexagonal grid. Electron. J. Co mbin., 16(1):R113,2009.[5] Iiro Honkala and Antoine ... twoways. On the one hand, each column can contain at most brones since each codeword occursin Br(vi) for at most brvertices. Thus, the total number of ones is at most br· K.Counting ones...

Báo cáo toán học: "Lower Bounds for the Average Genus of a CF-graph" doc

... a rotation system on G and R′be a rota t io n system on G′. Let Γ and Γ′be the sets of rotation system on G and G′respectively. We denote ΓR′the set ofall rotation systems on G that ... ScienceFoundation of China under Grant No. 10901048.References[1] D. Archdeacon, Calculations on the average genus and genus distribution of graphs,Congr. Numer. 67 (1988) 114–124.[2] D. Archdeacon, ... section. Let G′be a subgraph of agraph G and R be a rotation system on G. The induced rotation system R′ on G′isobtained by deleting all edges of G − G′from the rotation system R. Let Γ and...

Báo cáo toán học: " A note on edge-colourings avoiding rainbow K4 and monochromatic Km" doc

... 2: A rotational Hamilton cycle in L3(bold). on ℓjif and only if αi, αj and αj+1are linearly dependent in V . Assuming thiscondition holds, it is clear t hat αi+1, αj+1 and αj+2are ... pilies on a line ℓj, then pi+1lies on ℓj+1. A key observation is that piliesthe electronic journal of combinatorics 16 (2009), #N19 6A note on edge-colourings avoiding rainbow K4 and monochromatic ... thatpoints and lines of PG(2, q) correspond one-to-one to subspaces of V of dimension1 and 2, r espectively. In particular, for i = 0, . . . , q2+ q, let pibe the point ofP G(2, q) corresponding...

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