Báo cáo toán học: " Cyclic Sieving Phenomenon in Non-Crossing Connected Graphs" pps

... 10.1]. 6.1 Cyclic sieving phenomenon in other types of graphs In [3], one finds various formulas f or counting classes of non-crossing graphs, of which (1) is one. Consider the following four generating ... let C be the cyclic g roup of order n acting on X by rotation. Then (X, X(q), C) exhibits the cyclic sieving phenomen o n. 6.2 Unifying algebraic proof of cyclic sievin...

Ngày tải lên: 08/08/2014, 12:23

... having at most 100 points. 9 Concluding remarks. 9.1. Classical Seidel’s switching is certainly the first origin of this paper. It goes back to the paper [vLinS66]. Explicitly the notion was introduced ... purpose we were using the following functions from COCO: ind, cgr, inm, sub,andaut. We describe below each of these functions. • ind input1.gen input2 output1.gen output2.map Starting from p...

Ngày tải lên: 07/08/2014, 07:21

... Cambridge, 2002 (Chapter 6). [RSW] V. Reiner, D. Stanton and D. White: The cyclic sieving phenomenon, J. Combin. Theory Ser. A 108 (2004), no. 1, 17–50. [Rh] B. Rhoades: Cyclic sieving, promotion, and representation ... expressible as X(q) =  x∈X q s(x) , where s is an intrinsically defined statistic for the elements of X. Indeed, nearly all known instances of the cyclic sieving...

Ngày tải lên: 08/08/2014, 12:22

... vertices are joined by an edge if and only if they differ in exactly one coordinate or they differ in all coordinates. An edge is in color j (1 ≤ j ≤ k − 1) if and only if its two ends differ in exactly ... Tuza, Rainbow Hamiltonian paths and canonically colored sub- graphs in infinite complete graphs, Mathematica Pannonica 1 (1990), 5–13. [7] P. Erd˝os and Zs. Tuza, Rainbow subgraphs...

Ngày tải lên: 07/08/2014, 13:21

... endpoints x, y. As C is closed, every point in P \ C is contained in a C-arc in P. Suppose no C-arc in P is a shortcut of C. We can find a family (W i ) i∈N of countably many internally disjoint ... disjoint arcs in P , such that fo r every i, W i is either a C-arc or an arc cont ained in C, and every edge in P lies in some W i (there may, however, exist ends in P that are no...

Ngày tải lên: 08/08/2014, 01:20

... vertices. A connected graph is called biconnected, if it remains connected after the removal of any vertex. A biconnected component of a graph is a maximal biconnected subgraph. In particular, a single ... cent to v 1 in Avo ider’s graph at this point. For 2  i  k, in the beginning of the i- t h subphase, Avoider chooses the vertex v i ∈ V i−1 of minimal degree in Enfor cer’s gr...

Ngày tải lên: 08/08/2014, 12:22

... partitioned into 2m cells X x , x ∈ X of d points. Analogously Y is represented as dκm points partitioned into 2κm cells Y y , y ∈ Y of d/2 points. To construct Λ d we take a random pairing of X into ... and (ii) g(x, y) < 0 for all points in {(x, y) ∈ ∂T : y ≤ 1/2(3 + 2κ)}. Solving the equation ∂g ∂y (x, y) = 0 for x, noting that the equation is linear in x, we obtain x = y(1 − y) ((d...

Ngày tải lên: 08/08/2014, 12:23

... points. Then there exists a block that is disjoint from X . Proof. Let y be a point in the STS(v) which is not in X . Then, since v ≥ 19, there exist at least nine blocks containing y and, since ... removing a point and all the blocks containing it; in this case a point of degree at most 4. What remains is a configuration containing 17 or more triples on 12 or fewer points, again 5-spars...

Ngày tải lên: 07/08/2014, 13:21

... the arcs outgoing from v) and the incoming color set of v (i.e. the set of colors of the arcs incoming to v), respectively. The drawing conventions for a configuration are the following: a vertex ... good QR 7 -arc-coloring of H. Suppose now that H  1 contains a special cycle C. The graph H  1 contains three 2- vertices. Since a special cycle consists in k pairs of 2-sources and 2-sinks, C...

Ngày tải lên: 07/08/2014, 13:21

... isolated ones in A corresponds to a matching in G with the property that the subgraph induced by the matching is K 2,2 -free. This implies that the edges of the matching cannot be in any biclique ... and biclique coverings and factorizations of (0, 1)-matrices, Bulletin of the I.C.A. 14 (1995) 17-86. [16] J. Orlin, Contentment in graph theory: covering graphs with cliques, Indag. Math...

Ngày tải lên: 07/08/2014, 13:21