MarriageTheoremのこと

_ プレプリント確認状況：arXiv:math 3月4日分まで、IACR ePrint 2012/451まで

_ 気になった論文１：Some Characterizations of a Normal Subgroup of a Group (Vipul Kakkar, R. P. Shukla, arXiv:1202.5626)

Let G be a group and H be a subgroup of G which is either finite or of finite index in G. In this note, we give some characterizations for normality of H in G. As a consequence we get a very short and elementary proof of the Main Theorem of [5], which avoids the use of the classification of finite simple groups

_ 気になった論文２：Chordal Graphs are Fully Orientable (Hsin-Hao Lai, Ko-Wei Lih, arXiv:1202.5718)

Suppose that D is an acyclic orientation of a graph G. An arc of D is called dependent if its reversal creates a directed cycle. Let m and M denote the minimum and the maximum of the number of dependent arcs over all acyclic orientations of G. We call G fully orientable if G has an acyclic orientation with exactly d dependent arcs for every d satisfying m <= d <= M. A graph G is called chordal if every cycle in G of length at least four has a chord. We show that all chordal graphs are fully orientable.

_ 気になった論文３：Automorphisms of geometric structures associated to Coxeter groups (Graham White, arXiv:1202.6441)

In this paper, we consider the automorphism groups of the Cayley graph with respect to the Coxeter generators and the Davis complex of an arbitrary Coxeter group. We determine for which Coxeter groups these automorphism groups are discrete. In the case where they are discrete, we express them as semidirect products of two obvious families of automorphisms. This extends a result of Haglund and Paulin.