Báo cáo toán học: "f -Vectors of 3-Manifolds" ppsx

... triangulation of M with f 0 vertices and f 1 edges. Proof: The lemma is a reformulation of Walkup’s Lemmas 7.3 from [46]. The con- dition of the existence of an Hamiltonian cycle in the link of some ... facet of a triangulated d-manifold K is a subset σ of the vertex set of cardinality d + 1 such that σ /∈ K, but every proper subset of σ is a face of K. Definition 15 Let K...

Ngày tải lên: 08/08/2014, 01:20

... characterization of h-vectors of Buchsbaum complexes of a special type including all 2-dimensional connected Buchs- baum complexes, and proved the necessity of the conjecture. The main result of this ... Betti numbers of ∆ (over K). The link of ∆ with respect to F ∈ ∆ is the simplicial complex lk ∆ (F ) = {G ⊂ [n] \F : G ∪F ∈ ∆}. In the study of face vectors of simplicial co...

Ngày tải lên: 07/08/2014, 21:21

... size m and d σ is the total weight of the smallest subtree of T which contains the leaves in σ. By the total weight of a tree, we mean the s um of the weights of all the edges in that tree. Definition ... called the m-dissimilarity vector of T . The set of all m-dissimilarity vectors of phylogenetic trees with n leaves will be called the space of m-dissimilarity vectors of...

Ngày tải lên: 08/08/2014, 01:20

... symbol of σ.Sincen +1>m, we can select a random subsequence of σ of length m by first throwing out one of the n + 1 symbols of σ at random and then randomly selecting a subsequence of length ... the following theorem of Stromquist. We give a proof which is somewhat shorter than the proof in [1], both for its own interest and because we will reuse the method of proof when stu...

Ngày tải lên: 07/08/2014, 08:22

... proof of Theorem 1. Lemma 7. Let P be a hereditary property of tournaments. If B(P) = ∞, then P contains arbitrarily large structures of Type 1 or 2. Proof. Let P be a hereditary property of ... proof of Theorem 28 of [4] can also be adapted to hereditary properties of tour- naments, to produce many properties with different exponential speeds, but we spare the reader the details...

Ngày tải lên: 07/08/2014, 15:23

... set X of b − 1 vertices, each of degree n − 1, a clique L of p 2 vertices, a the electronic journal of combinatorics 15 (2008), #R118 7 Saturation Numbers of Books Guantao Chen ∗ Dept. of Math. ... has a set X of b−1 vertices, each of degree n − 1, a clique L of p 2 vertices, a set T of n − p/2 − b + 1 vertices inducing an almost (p − 1)-regular graph which contains a vert...

Ngày tải lên: 07/08/2014, 21:20

... bijection between sets of w minimally dependent vectors among the columns of H and (q − 1)-tuples of vectors of weight w in V , where a tuple consists of all nonzero multiples of a weight w vector. Since ... elements of S ∩ P k . Hence |S ∩ P k |α ≥ β|S ∩ P k+1 |. Dividing the left side by the left side of (4) and the right side by the right side of (4) proves the claim. Let...

Ngày tải lên: 07/08/2014, 06:20

... h ∗ -vectors as well as the proof of Theorem 1.3. The notion of triangulation of a polytope P we will use does not require that all vertices of the triangulation are necessarily vertices of P ... that ∆ is a triangulation of a polytopal complex F if the union of the faces of ∆ is equal to the union of the faces of F and every face of ∆ is contained in a face of F.I...

Ngày tải lên: 07/08/2014, 08:22

... be viewed as a generalization of the size of F . Define ex f (n, F ) to be the maximal value of e f (G)overallF -free graphs G of order n. This mimics the definition of the usual Tur´an function ... possible in the sense that both of these operations are necessary. The paper is organized as follows. We present two different proofs of Theorem 1. The first proof, in Section 3, goes vi...

Ngày tải lên: 07/08/2014, 13:21

... copy of u 1 to the last copy of u l+1 , and number its vertices by 1, . . . , lt + 1 in the natural order, from the copy of u 1 in the first copy of F to the copy of u l+1 in the last copy of F ... tree Y s uch that s(F, Y ) ≡ 0 (mod m). Proof. Let W t be a tree made of t copies of F in which we identify the vertex u l+1 of copy i with the vertex u 1 of copy i + 1 ( for 1 ≤...

Ngày tải lên: 08/08/2014, 12:23