Algorithmic Recognition of Group Actions on Orbitals

MOP - Algorithmic Modality Analysis for Parabolic Group Actions

Group Actions on Partitions

We introduce group actions on the integer partitions and their variances. Using generating functions and Burnside’s lemma, we study arithmetic properties of the counting functions arising from group actions. In particular, we find a modulo 4 congruence involving the number of ordinary partitions and the number of partitions into distinct parts.

Group Actions on Posets

In this paper we study quotients of posets by group actions. In order to define the quotient correctly we enlarge the considered class of categories from posets to loopfree categories: categories without nontrivial automorphisms and inverses. We view group actions as certain functors and define the quotients as colimits of these functors. The advantage of this definition over studying the quoti...

Group Actions on Trees

For this paper, we will define a (non-oriented) graph Γ to be a pair Γ = (V,E), where V = vert(Γ) is a set of vertices, and E = edge(Γ) ⊆ V × V/S2 is a set of unordered pairs, known as edges between them. Two vertices, v, v′ ∈ V are considered adjacent if (v, v′) ∈ E, if there is an edge between them. An oriented graph has edge set E = edge(Γ) ⊆ V × V , ordered pairs. For an edge v = (v1, v2) i...

On Partitioning the Orbitals of a Transitive Permutation Group

Let G be a permutation group on a set Ω with a transitive normal subgroup M . Then G acts on the set Orbl(M,Ω) of nontrivial M -orbitals in the natural way, and here we are interested in the case where Orbl(M,Ω) has a partition P such that G acts transitively on P. The problem of characterising such tuples (M,G,Ω,P), called TODs, arises naturally in permutation group theory, and also occurs in ...