Báo cáo toán học: "The Cyclic Sieving Phenomenon for Faces of Cyclic Polytope" docx

... electronic journal of combinatorics 17 (2010), #R47 13 The Cyclic Sieving Phenomenon for Faces of Cyclic Polytopes Sen-Peng Eu ∗ Department of Applied Mathematics National University of Kaohsiung, ... ove the cyclic sieving phenomenon, introduced by Reiner-Stanton- White, for faces of an even-dimensional cyclic polytope, under a group action that cyclically tr...

Ngày tải lên: 08/08/2014, 12:22

... Sidorenko [18] for a full discussion of this problem. For a general hypergraph F Sidorenko [19] (see also [20]) obtained a bound for the Tur´an density in terms of the number of edges, showing ... a forest of given size. Lemma 2 (i) An r-uniform hypergraph with at least r!(t − 1) r edges contains a forest with t edges. (ii) Let F be a 3-uniform hypergraph. Then either (a) F cont...

Ngày tải lên: 07/08/2014, 08:22

Ngày tải lên: 05/08/2014, 10:20

Ngày tải lên: 05/08/2014, 15:21

... x 0 (t) of the perturbed system (3.1) is a solution of some linear system of form (3.3),whereF (t)x is of the same order of smallness as f (t, x), i.e. F (t)  δ(t), ∀t ∈ R + . (3.4) Proof. From ... R(t)isaC-function of im P(t) of (3.11). Thus, C-classes R of (2.1) and R U imP of the invariant subspace im P of the solution space of (3.11) coincide. Suppose that x δ (t)...

Ngày tải lên: 06/08/2014, 05:20

... 4-coloring of G, and hence c uses both colors on K. Therefore, c is a 2-coloring of H(G). For the skeptics of the proof of the 4-Color Theorem and since we do not want to use this powerful theorem for ... standard application of Euler’s formula shows that  i≥0 (4 − i)n i +  i≥0 (4 − i)f i =8 (1) where n i is the number of vertices of degree i and f i is the number of fac...

Ngày tải lên: 07/08/2014, 06:20

... boundary of the edge set of a cycle is empty. The boundary of the set of 4-cycles of a cube is also empty, as is the boundary of any set of vertices. For j ≥ 1, define a j- N circuit to be any set S of ... boundary of an edge consists of its two endpoints, the boundary of a K 2,2 consists of the four edges of that 4-cycle, the boundary of a K 2,3 consists of its...

Ngày tải lên: 07/08/2014, 07:21

... the vertex sets of π are of size one or two. Finally, for k ≥ 3 a tip may be of arbitrary size thus a vertex set of π can be of arbitrary size as well. Because the ground set of the matroid M ... the maximum weight bases of M with the weight function X → | X| for X ∈ π. This weighted matroidal approach yields a proof for the Berge-type formula of [5] on the size of a...

Ngày tải lên: 07/08/2014, 08:22

... vertices of p a are completely joined to the vertices of p b in G. Proof. Assume (to reach a contradiction) that the lemma is false. Of all counterexamples, pick an optimal coloring C of G, {a}, ... all we need to check is that the union of any m − 2 of lists has at least m − 2 elements and that the union of all of the lists has m − 1 elements. If the former were false, then s...

Ngày tải lên: 07/08/2014, 15:22

... fixed distance d − i by moving “forward” i steps. For now, this will be presented in the form of the existence of the so-called conjugate polynomials p i of degree i, for i = 0, 1, . . . , d, with ... goal of this paper is to give an elementary and global proof of the spectral excess theorem. The original proof by Fiol et al. [13, 14] has a local approach and is quite technical b...

Ngày tải lên: 07/08/2014, 21:20