Báo cáo toán học: "Triangulations and the Haj´s Conjecture " ppt

... can go wrong. On the other hand, he observed that locally planar graphs and triangulations of the projective plane and the torus satisfy Haj´os Conjecture, and he conjectured that the same holds ... satisfy the Haj´os Conjecture? For a graph H and a positive integer t,let ˜ H t be the graph obtained from the union of H and the clique K t by adding all edges betwee...

Ngày tải lên: 07/08/2014, 08:22

... v-decomposition numbers are the coefficients obtained when the elements of the canonical basis are expanded in terms of the standard basis, i.e. the coefficients d λµ (v) in the expression G(µ) =  λ d λµ (v)λ. We ... v-decomposition numbers; one con- cerning the Mullineux map, and the other concerning e-regularisation. The first of these involves the e-weight of a partition,...

Ngày tải lên: 07/08/2014, 21:21

... 4.2.5]. There are several equivalent but differently flavored characterizations of Golod rings, see Sections 5.2 and 10.3 in [1] and the references therein. One is that R is Golod if the ranks of the ... order of the facets of ∆ ∨ . The complements F 1 c , . . . , F r c are the minimal non-faces of the flag complex ∆, so |F i c | = 2 and |F i | = |V |−2 for all i. Let j ≥ 2...

Ngày tải lên: 08/08/2014, 01:20

... =0, and if n is odd, then AT(n) = 0and AT(n +1)=0=⇒AT(2n) =0. Together, these imply the truth of the Alon-Tarsi conjecture for n =2 r (p+1) for any r ≥ 0 and any odd prime p (and, by the table ... ols(n), fdels(n), and fdols(n), respectively. If n = 1 is odd, then switching two rows of a latin square alters its sign, so els(n)=ols(n). On the other hand, Alon and Tarsi...

Ngày tải lên: 07/08/2014, 06:22

... the space DT endowed with the operations ≺, , and ·. Then (DT λ , ) is the initial object in λ . In the above definitions, we have set H(x)=(x 1 , ,x n )andH(y)=(y 1 , ,y m ), and G and H stand ... We calculate the dimensions of the homogeneous components of these algebras (with respect to a bidegree related to the number of nodes and the number of angles in the tree...

Ngày tải lên: 07/08/2014, 13:21

... weight to use, and the third coordinate is given by i + j = k + c. These NIPs move exactly a steps in one direction and b steps in the other. NIPs are free fermions, and therefore their propagator ... d and c + d + e are frozen, and once these are removed one obtains the tiling with a → a − 1. Similarly, if t 1 = q −2 z 1 , the first rows of the sides of lengths b + c and...

Ngày tải lên: 07/08/2014, 13:21

... Second, suppose the square which is being removed from λ i−1 , is at the end of row  and contains the entry x. Then we remove the square and RSK-insert x into the ( − 1)-th row in the square which ... of predicting the spatial configuration of a molecule. For RNA this means to understand the configuration of the primary sequence composed by the four nucleotides A, G, U...

Ngày tải lên: 07/08/2014, 21:20

... Hahn and Jackson conjectured that this theorem is best possible in the following strong sense. For each positive integer k, there is a digraph D with stability number k such that deleting the ... Dilworth’s theorem [4] that the size of a maximum antichain in a partially ordered set is equal to the minimum number of chains needed to cover it. In 1990, Hahn and Jackson [8] conjectur...

Ngày tải lên: 07/08/2014, 21:21

... graphs and prove analogues of Brooks’ Theorem for both the distinguishing number and the chromatic distinguishing number. In this paper we approa ch the subject from the perspective of group theory ... If J 1 and J 2 are colored identically then there is a non-trivial automorphism of G that interchanges J 1 and J 2 and preserves the colors, a contradiction. Otherwise, by R...

Ngày tải lên: 08/08/2014, 01:20

... of the side AB and M, and F be the common point of the side CD and M. Then it’s obvious that |EF | < l 2 and v sin β ≤ |EF |, so v ≤ l 2 sin β . In the same way, we get u ≤ l 2 sin β . By the ... K. Theorem A. ([2]) Let C be the unit square and let ε be equal to 1 − 1/ √ 2 ≈ 0.29. If εC lies in the interior of the square C and the annulus C\εC is covered by fin...

Ngày tải lên: 07/08/2014, 15:22