Crystallographic arrangements: Weyl groupoids and simplicial arrangements

We introduce the simple notion of a "crystallographic arrangement" and prove a one-to-one correspondence between these arrangements and the connected simply connected Cartan schemes for which the real roots are a finite root system (up to equivalence on both sides). We thus obtain a more accessible definition for this very large subclass of the class of simplicial arrangements for which a complete classification is known.Comment: 13 page

Bigraphical Arrangements

We define the bigraphical arrangement of a graph and show that the Pak-Stanley labels of its regions are the parking functions of a closely related graph, thus proving conjectures of Duval, Klivans, and Martin and of Hopkins and Perkinson. A consequence is a new proof of a bijection between labeled graphs and regions of the Shi arrangement first given by Stanley. We also give bounds on the number of regions of a bigraphical arrangement.Comment: Added Remark 19 addressing arbitrary G-parking functions; minor revision

Voluntary Environmental Governance Arrangements

Voluntary environmental governance arrangements have focal attention in studies on environmental policy, regulation and governance. The four major debates in the contemporary literature on voluntary environmental governance arrangements are studied. The literature falls short of sufficiently specifying whether or not voluntary environmental governance arrangements are successful in addressing environmental risks. This is due to the narrow focus of many contemporary studies and a tendency to study the form and content of voluntary environmental governance arrangements in isolation from their contextual settings. In order to gain a better understanding of voluntary environmental governance arrangements, scholars are challenged to study differently structured voluntary environmental governance arrangements in different contextual settings, to move beyond single country or single voluntary environmental governance arrangements studies, and to combine quantitative and qualitative data in studying these arrangements

The classification of musical transformation: a conceptual approach to the knowledge organization of musical arrangements

Introduction. The purpose of this paper is to provide a conceptual analysis of the knowledge organization of musical arrangements found in notated Western art music. Analysis. Four areas of arrangements are analysed. Inter-medium arrangements are explored, which are arrangements that transform one musical medium into another. Arrangements which involve changes of difficulty or pitch are discussed, as well as transformations between notation and performance. Arrangements of forms and genres are analysed, including sub-genres such as literal transcriptions, fantasies, virtuosic arrangements and pot-pourris. The function of arrangements is also discussed. Results. This study introduces additional facets, foci and types of information. These include the development of musical themes as a classification principle, the concept of a performancearrangement, and the idea of functions specifically associated with transformation. A categorisation is proposed for the various types of form/genre arrangements, which shows blurred boundaries between types. The impact of time on arrangements is demonstrated, and that there is a non-binary division between the original and the arranged. Conclusion. Two models demonstrate the complexities of musical arrangement, and how information specific to arrangements needs to be considered within music knowledge organization. Furthermore, the results suggest novel ideas about classifying change and transformation more generally