Editorial: Mapping power in adult education and learning

Power is […] a contested terrain where different notions of power are put into play and debated by researchers. And current change in adult education and learning policies and practices calls for further such debate. We have used the concept of ‘mapping’ as part of the title for this thematic issue, so as to signify the need to map power, i.e. to describe the working of power within practices of adult education and learning. To create debate, there is a need for ‘description’, made by drawing on the different theorizations of power. For this thematic issue we have thus invited papers that engage in mapping power in adult education and learning. (DIPF/Orig.

Strongly primitive species with potentials I: Mutations

Motivated by the mutation theory of quivers with potentials developed by Derksen-Weyman-Zelevinsky, and the representation-theoretic approach to cluster algebras it provides, we propose a mutation theory of species with potentials for species that arise from skew-symmetrizable matrices that admit a skew-symmetrizer with pairwise coprime diagonal entries. The class of skew-symmetrizable matrices covered by the mutation theory proposed here contains a class of matrices that do not admit global unfoldings, that is, unfoldings compatible with all possible sequences of mutations.Comment: 51 page

The Mathematics of Chinese Checkers

Our goal for this project was to expand and improve upon the findings of George I. Bell and Nicholas Fonseca, who have both written papers on optimization in Chinese Checkers. While their work focuses mainly on cooperative games between one, two, and three players, we have considered games for six players. While doing this, we have redefined the playing board in a more intuitive manner, while developing and proving its associated distance formula. As well, we have found the shortest game for six players, and are working to generalize a formula for the number of moves required to finish a six player game as fast as possible. This could further incite research to generalize a lower bound for any number of players

Editorial: open issue

In this open issue we present five papers covering different adult education and learning contexts across different geographical spaces, ranging from Spain, Germany, Eastern Europe to Canada. The topics of research range from young people to retired people, adult educators and men and women reading self-help literature

Quivers with potentials associated to triangulated surfaces

We attempt to relate two recent developments: cluster algebras associated to triangulations of surfaces by Fomin-Shapiro-Thurston, and quivers with potentials and their mutations introduced by Derksen-Weyman-Zelevinsky. To each ideal triangulation of a bordered surface with marked points we associate a quiver with potential, in such a way that whenever two ideal triangulations are related by a flip of an arc, the respective quivers with potentials are related by a mutation with respect to the flipped arc. We prove that if the surface has non-empty boundary, then the quivers with potentials associated to its triangulations are rigid and hence non-degenerate.Comment: v3: 44 pages, 57 figures. Prop 29 of v2 generalized to Thm 36, some changes to References. In response to referee's comments: some examples added, more cases verified in proof of Thm 30 (formerly Thm 23). Submitted to Proc. London Math. So