Báo cáo toán học: "Two New Extensions of the Hales-Jewett Theorem" pdf

... ···<A n .In other words, the function γ restricted to the standard n 2 -variable submatrices of v is the lift of an r-coloring γ  of the set  F({1, ,L})  n < . By the choice of L, there thus exist ... regular words (that is, elements of W M k ) 0-variable words, then the Hales-Jewett theorem corresponds to the case n =0,t = 1 of Theorem 1.4. Theorem 1.4 Le...

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... is to show that the ratio 3/8 in Reed’s Theorem 2 holds if we relax the minimum degree condition from three to two, but restrict the structure of the graph the electronic journal of combinatorics ... neighborhood of v is the set N(v) = {u ∈ V | uv ∈ E} and the closed neighborhood of v is N[v] = {v} ∪ N(v). For a set S of vertices, the open neighbor hood of S is defi...

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... we get the first term if the last letter of the Fibonacci word is a. If the last letter is b we need the following result of [6]: the electronic journal of combinatorics 10 (2003), #R19 3 The above ... But there is a more illuminating combinatorial proof of (3.1 ), which is an adapta- tion of Franklin’s proof of the pentagonal number theorem to this case (cf. [1] or...

Ngày tải lên: 07/08/2014, 07:21

... sequence of transpositions, then the poly- nomial (1) is equal to a sum of polynomials of the form (2) and again is TNN. (⇐) Suppose that π is not less than or equal to σ in the Bruhat order. By Theorem ... sequence of transpositions, then the evaluation of (3) at A is equal to a sum of polynomials of the form (4) and again (3) is SNN. (⇐) Suppose that π is not less th...

Ngày tải lên: 07/08/2014, 08:20

... S λ is the Schur function corresponding to λ, ST(λ) denotes the collection of stan- dard tableaux of shape λ, co(T ) denotes the cocharge of T and c λ gives the sum of the contents of the partition ... QI m (D n ) of m-quasi-invariants of D n . More precisely we have the electr onic jou rnal of combinatorics 12 (2005), #R20 8 Proof Because of uniqueness of t...

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... in the tables. The column NewBest indicates a new best result. The meaning of the annotations is given in the Key. The tables show the relative merits of the general algorithms in terms of the ... which give further increases in the number of codewords in specific cases. Thus the tables allow a general comparison of the merits of the chosen algorithms. T...

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