Báo cáo toán học: "A Paintability Version of the Combinatorial Nullstellensatz, and List Colorings of k-partite k-uniform Hypergraphs" pps

... respectively down to ⌈ ⌉ ⌊ ⌋ the electronic journal of combinatorics 17 (2010), #R176 5 A Paintability Version of the Combinatorial Nullstellensatz, and List Colorings of k-partite k-uniform Hypergraphs Uwe ... ame-theoretic setting in Section 4. The definitions and proofing ideas in this section generalize the introduction of paintability of graphs in [S...

Ngày tải lên: 08/08/2014, 12:23

... denote the vertices of the graph C r by the elements of {1, 2, , r}. Since the images of the vertices have cardinality two in our case, we denote the vertices and so their weights by x i and (1 ... the symmetry of Bethe-trees, one can express the weights of the optimal construc- tion of a Bethe-tree, starting from the root, level by level, recursively, in t...

Ngày tải lên: 08/08/2014, 12:23

... +32t − 1. Then f(n) ≥ n +32t − 1, for n ≥ n t . This completes the proof of the theorem. From the above theorem, we have lim inf n→∞ f(n) − n √ n ≥  2+ 2562 6911 , which is better than the previous ... denote the number of vertices, and (G) denote the number of edges. In this paper, we construct a graph G having no two cycles with the same length which leads to the f...

Ngày tải lên: 07/08/2014, 06:22

... s 2 n . (1) where b(i) is the number of times the integer i occurs in the sequence T . Note that the sum of all b(i), 1 ≤ i ≤ n,isequaltol, the length of T . 3 A simple proof for the existence of exponentially balanced ... u R 1 ,n+1,u 1 ,n+2,u R 1 ,j 0 , u R 0 ,n+2,u 0 ,n+1,u R 0 ,n+2, is the transition sequence of an (n +2)-bit Gray code. In the proof of Theorem...

Ngày tải lên: 07/08/2014, 08:22

... and j = c − 1. Again using the fact that λ and µ agree above row r and to the left of column c (and the definitions of r and c) we see that the only possibility for λ/µ is (r, c), completing the proof ... 1 rows of λ and µ agree. Now note that λ has more than 2k cells to the right of column k, so there are k-deletions of λ in which the removed cells all lie t...

Ngày tải lên: 07/08/2014, 15:22

... : the uppermost cell of the rightmost column of the polyomino has the maximal ordinate among all the cells of the polyomino; U2 : the lowest cell of the rightmost column of the polyomino has the ... (k) g (k) g . The root of the tree is (1) b , which is the label of the one-cell polyomino. the electronic journal of combinatorics 14 (2007), #R57 11...

Ngày tải lên: 07/08/2014, 15:22

... φ((π, f)) = (π, f). Otherwise, let (i, j) ∈ R (π,f) be minimal under the lexicographic ordering of R (π,f) . Let ˜π = (i, j) ◦ π, the product of the transposition (i, j) and π in S n . Note that, ... finally that (π, f) = φ((π, f )) if and only if R (π,f) = ∅, or if and o nly if κ(π) = n (so π = e n , the identity permutation of S n ) and f : K π → A is injective. Therefo...

Ngày tải lên: 08/08/2014, 01:20

... where des(σ) and inv(σ) denote, resp ectively, the descent number and inversion number of σ in the symmetric group S n of degree n. We give an algebraic proof and a combinatorial proof of the recurrence ... + n−1  k=1  n k  A n−k (t)A k (t), satisfied by the classical Eulerian polynomials A n (t) :=  σ∈S n t des(σ) . 3 A combinatorial proof We give a combinatorial...

Ngày tải lên: 08/08/2014, 11:20

... advantage of the mixing property we can now infer without much effort the behaviour of the asymptotic variance and also deduce the asymptotic normality of the statistic LA n (µ) . This is done in the ... study the asymptotic behaviour of LA n (a). As a matter of notation, we will use generically, the expression LA n (µ) for the distribution of the length of...

Ngày tải lên: 08/08/2014, 12:23

... may not be present in H G and where the degrees of the vertices of H G different from x u , x v and w are unchang ed in G. Further, V (H G ) ∩ X = ∅ and ea ch of x u , x v and w is adjacent in G ... size m = |E|, and let v be a vertex in V . The open 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...

Ngày tải lên: 08/08/2014, 12:23