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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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Koszulity, supersolvability and Stirling Representations [PDF]
Supersolvable hyperplane arrangements and matroids are known to give rise to certain Koszul algebras, namely their Orlik–Solomon algebras and graded Varchenko–Gel’fand algebras. We explore how this interacts with group actions, particularly for the braid
Reiner, Victor +2 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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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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Coprime actions with supersolvable fixed-point groups
, 2018 Let A be an elementary abelian r-group acting on a finite r ′
Hangyang Meng, Xiuyun Guo
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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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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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Supersolvable saturated matroids and chordal graphs
, 2023 A matroid is supersolvable if it has a maximal chain of flats each of which is modular. A matroid is saturated if every round flat is modular. In this article we present supersolvable saturated matroids as analogues to chordal graphs, and we show that ...
Probert, Andrew, Mayhew, Dillon
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