Search results for "Combinatorics"
showing 10 items of 1770 documents
A reduction theorem for a conjecture on products of two π -decomposable groups
2013
[EN] For a set of primes pi, a group X is said to be pi-decomposable if X = X-pi x X-pi' is the direct product of a pi-subgroup X-pi and a pi'-subgroup X-pi', where pi' is the complementary of pi in the set of all prime numbers. The main result of this paper is a reduction theorem for the following conjecture: "Let pi be a set of odd primes. If the finite group G = AB is a product of two pi-decomposable subgroups A = A(pi) x A(pi') and B = B-pi x B-pi', then A(pi)B(pi) = B(pi)A(pi) and this is a Hall pi-subgroup of G." We establish that a minimal counterexample to this conjecture is an almost simple group. The conjecture is then achieved in a forthcoming paper. (C) 2013 Elsevier Inc. All ri…
A note on a result of Guo and Isaacs about p-supersolubility of finite groups
2016
In this note, global information about a finite group is obtained by assuming that certain subgroups of some given order are S-semipermutable. Recall that a subgroup H of a finite group G is said to be S-semipermutable if H permutes with all Sylow subgroups of G of order coprime to . We prove that for a fixed prime p, a given Sylow p-subgroup P of a finite group G, and a power d of p dividing such that , if is S-semipermutable in for all normal subgroups H of P with , then either G is p-supersoluble or else . This extends the main result of Guo and Isaacs in (Arch. Math. 105:215-222 2015). We derive some theorems that extend some known results concerning S-semipermutable subgroups.
On self-normalising subgroups of finite groups
2010
[EN] The aim of this paper is to characterise the classes of groups in which every subnormal subgroup is normal, permutable, or S-permutable by the embedding of the subgroups (respectively, subgroups of prime power order) in their normal, permutable, or S-permutable closure, respectively.
On a graph related to permutability in finite groups
2010
For a finite group G we define the graph $\Gamma(G)$ to be the graph whose vertices are the conjugacy classes of cyclic subgroups of G and two conjugacy classes $\{\mathcal {A}, \mathcal {B}\}$ are joined by an edge if for some $\{A \in \mathcal {A},\, B \in \mathcal {B}\, A\}$ and B permute. We characterise those groups G for which $\Gamma(G)$ is complete.
On extremal cases of Hopcroft’s algorithm
2010
AbstractIn this paper we consider the problem of minimization of deterministic finite automata (DFA) with reference to Hopcroft’s algorithm. Hopcroft’s algorithm has several degrees of freedom, so there can exist different executions that can lead to different sequences of refinements of the set of the states up to the final partition. We find an infinite family of binary automata for which such a process is unique, whatever strategy is chosen. Some recent papers (cf. Berstel and Carton (2004) [3], Castiglione et al. (2008) [6] and Berstel et al. (2009) [1]) have been devoted to find families of automata for which Hopcroft’s algorithm has its worst execution time. They are unary automata as…
A Graph Based Algorithm For Intersection Of Subdivision Surfaces
2003
Computing surface intersections is a fundamental problem in geometric modeling. Any boolean operation can be seen as an intersection calculation followed by a selection of the parts necessary for building the surface of the resulting object. A robust and efficient algorithm to compute intersection on subdivision surfaces (surfaces generated by the Loop scheme) is proposed here. This algorithm relies on the concept of a bipartite graph which allows the reduction of the number of faces intersection tests. Intersection computations are accelerated by the use of the bipartite graph and the neighborhood of intersecting faces at a given level of subdivision to deduce intersecting faces at the fol…
On block pumpable languages
2016
Ehrenfeucht, Parikh and Rozenberg gave an interesting characterisation of the regular languages called the block pumping property. When requiring this property only with respect to members of the language but not with respect to nonmembers, one gets the notion of block pumpable languages. It is shown that these block pumpable are a more general concept than regular languages and that they are an interesting notion of their own: they are closed under intersection, union and homomorphism by transducers; they admit multiple pumping; they have either polynomial or exponential growth.
On Coloring Unit Disk Graphs
1998
In this paper the coloring problem for unit disk (UD) graphs is considered. UD graphs are the intersection graphs of equal-sized disks in the plane. Colorings of UD graphs arise in the study of channel assignment problems in broadcast networks. Improving on a result of Clark et al. [2] it is shown that the coloring problem for UD graphs remains NP-complete for any fixed number of colors k≥ 3 . Furthermore, a new 3-approximation algorithm for the problem is presented which is based on network flow and matching techniques.
Branch and bound for the cutwidth minimization problem
2013
The cutwidth minimization problem consists of finding a linear arrangement of the vertices of a graph where the maximum number of cuts between the edges of the graph and a line separating consecutive vertices is minimized. We first review previous approaches for special classes of graphs, followed by lower bounds and then a linear integer formulation for the general problem. We then propose a branch-and-bound algorithm based on different lower bounds on the cutwidth of partial solutions. Additionally, we introduce a Greedy Randomized Adaptive Search Procedure (GRASP) heuristic to obtain good initial solutions. The combination of the branch-and-bound and GRASP methods results in optimal solu…
Balancing and clustering of words in the Burrows–Wheeler transform
2011
AbstractCompression algorithms based on Burrows–Wheeler transform (BWT) take advantage of the fact that the word output of BWT shows a local similarity and then turns out to be highly compressible. The aim of the present paper is to study such “clustering effect” by using notions and methods from Combinatorics on Words.The notion of balance of a word plays a central role in our investigation. Empirical observations suggest that balance is actually the combinatorial property of input word that ensure optimal BWT compression. Moreover, it is reasonable to assume that the more balanced the input word is, the more local similarity we have after BWT (and therefore the better the compression is).…