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

A note on statistical averages for oscillating tableaux

We define a statistic called the weight of oscillating tableaux. Oscillating tableaux, a generalization of standard Young tableaux, are certain walks in Young's lattice of partitions. The weight of an oscillating tableau is the sum of the sizes of all the partitions that it visits. We show that the average weight of all oscillating tableaux of shape lambda and length 2n plus the size of lambda has a surprisingly simple formula: it is a quadratic polynomial in the size of lambda and n. Our proof via the theory of differential posets is largely computational. We suggest how the homomesy paradigm of Propp and Roby may lead to a more conceptual proof of this result and reveal a hidden symmetry in the set of perfect matchings.Comment: 7 page

Can models of organizational change help to understand ‘success’ and ‘failure’ in community sentences? Applying Kotter’s model of organizational change to an Integrated Offender Management case study

A number of nationally driven initiatives have led to significant changes in the framework of community sentences, with various agencies being required to work in ‘joined-up’ multi-agency arrangements. Most notable, perhaps, has been the increased working relationship between police and probation, most recently within Integrated Offender Management (IOM). Although these have produced some positive outcomes in relation to crime reduction, success is sporadic and often quite modest. Research has identified a number of barriers to successful implementation, and this article builds on this by drawing upon fresh empirical evidence to argue that the success of such schemes relies on the management of organizational change that will inevitably and necessarily occur. Applying Kotter’s model of organizational change to data generated from an evaluation of two IOM schemes in England, the article offers an explanatory account of the implementation of the schemes and the possible effect this had on efforts to reduce crime

On Objects as Events and the Ontology of Temporal Parts

Temporal parts pose something of a quandary. On the one hand, if they exist and fulfill the roles they are frequently claimed to, they appear to be an elegant solution to a number of basic metaphysical problems, change and identity of an object through time foremost, but also a number of smaller (perhaps subsidiary) issues. But on the other hand, an account of their ontology (not the ontology of things the temporal-parts theorist claims they compose) is not easily intuitively forthcoming. The questions of just exactly what a temporal part is and why we ought to believe they exist are troubling indeed. I will here briefly rehash the conventional view on the ontology of temporal parts, raise a few of the choiciest problems it faces in the cogency of the existence of temporal parts as entities of the sort that can solve the metaphysical problems in question (or indeed as entities at all), and offer my own alternative view. In the end, we will see that temporal parts can be constructed from the more fundamental notion of events and so become theoretical entities that nonetheless can do the heavy philosophical lifting we expect of them