Results 31 to 40 of about 366,411 (69)
Combinatorial generation via permutation languages. VII. Supersolvable hyperplane arrangements
European Journal of CombinatoricsFor an arrangement $\mathcal{H}$ of hyperplanes in $\mathbb{R}^n$ through the origin, a region is a connected subset of $\mathbb{R}^n\setminus\mathcal{H}$. The graph of regions $G(\mathcal{H})$ has a vertex for every region, and an edge between any two vertices whose corresponding regions are separated by a single hyperplane from $\mathcal{H}$.
Sofia Brenner +4 more
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CONSTRUCTION OF TRANSITIVE SUPERSOLVABLE PERMUTATION GROUPS [PDF]
, 2018 In this paper, we used wreath products of two permutation groups in constructing transitive supersolvable permutation groups. We verified these groups using some groups theoretical concepts and also validate our work using a standard program; GAP ...
Musa, Sani +3 more
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Hamiltonian Cycles in Simplicial and Supersolvable Hyperplane Arrangements
Motivated by the Gray code interpretation of Hamiltonian cycles in Cayley graphs, we investigate the existence of Hamiltonian cycles in tope graphs of hyperplane arrangements, with a focus on simplicial, reflection, and supersolvable arrangements. We confirm Hamiltonicity for all 3-dimensional simplicial arrangements listed in the Grünbaum--Cuntz ...
Körber, Veronika +3 more
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A Generalization of Semimodular Supersolvable Lattices
, 1999 Stanley [18] introduced the notion of a supersolvable lattice, L, in part to combinatorially explain the factorization of its characteristic polynomial over the integers when L is also semimodular.
Bruce E. Sagan, Curtis Bennett
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Nice Partitions, Supersolvability, and Freeness in Deformations of Graphic Arrangements
We study affine deformations $\mathcal{A}(G_{\mathcal{S}})$ of graphic arrangements and their cones. Here $G=([n],E(G))$ is a simple graph, $\mathcal{S}=(S_{ij})$ is a family of finite gain sets, and $\mathcal{A}(G_{\mathcal{S}})$ consists of the hyperplanes $x_i-x_j=a$ with $a\in S_{ij}$.
Liang, Weikang, Wang, Suijie, Zhou, Yue
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Koszul Orlik--Solomon Algebras from Non-supersolvable Arrangements
The cohomology ring of the complement of a complex hyperplane arrangement is given by its Orlik--Solomon algebra. It is known that the defining ideal of the Orlik--Solomon algebra has a quadratic Gröbner basis in the standard presentation if and only if the intersection lattice is supersolvable; such algebras are automatically Koszul.
Le, Tuong +2 more
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Indices of non-supersolvable maximal subgroups in finite groups
Two classic results, due to K. Doerk and P. Hall respectively, establish the solvability of those finite groups all of whose maximal subgroups are supersolvable, and the solvability of finite groups in which all maximal subgroups have prime or squared ...
Beltrán, Antonio, shao, Changguo
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Groups with supersolvable automorphism group [PDF]
We call a finite group G ultrasolvable if it has a characteristic subgroup series whose factors are cyclic. It was shown by Durbin--McDonald that the automorphism group of an ultrasolvable group is supersolvable. The converse statement was established by
Sambale, Benjamin
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How Is a Chordal Graph Like a Supersolvable Binary Matroid?
, 2007 Let G be a finite simple graph. From the pioneering work of R. P. Stanley it is known that the cycle matroid of G is supersolvable i# G is chordal (rigid): this is an other way to read Dirac's theorem on chordal graphs.
Sulamita Klein +2 more
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Computing irreducible representations of supersolvable groups
, 1994 Recently, it has been shown that the ordinary irreducible representations of a supersolvable group G of order n given by a power-commutator presentation can be constructed in time O ( n 2
Ulrich Baum, Michael Clausen
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