Pattern classes and priority queues

When a set of permutations comprising a pattern class C is submitted as input to a priority queue the resulting output is again a pattern class C'. The basis of C' is determined for pattern classes C whose basis elements have length 3, and is finite in these cases. An example is given of a class C with basis 2431 for which C is not finitely based

Isomorphisms between pattern classes

Isomorphisms p between pattern classes A and B are considered. It is shown that, if p is not a symmetry of the entire set of permutations, then, to within symmetry, A is a subset of one a small set of pattern classes whose structure, including their enumeration, is determined.Comment: 11 page

Subclasses of the separable permutations

We prove that all subclasses of the separable permutations not containing Av(231) or a symmetry of this class have rational generating functions. Our principal tools are partial well-order, atomicity, and the theory of strongly rational permutation classes introduced here for the first time

Inflations of Geometric Grid Classes: Three Case Studies

We enumerate three specific permutation classes defined by two forbidden patterns of length four. The techniques involve inflations of geometric grid classes

Reframing Literacy in Adult ESL Programs: Making the case for the inclusion of identity

Adult  ESL  programs  in  the  Australian  context  are  heavily  influenced  by  neo-liberal notions  of  functional  literacy  and  numeracy.  This paper argues that such notions, designed to enable the learner to function within the workplace or community can fail to acknowledge the complexity of ESL program participation for adult learners. This may be considered especially so for pre-literate learners from refugee backgrounds who have low or minimal levels of literacy in their own language and are hence negotiating a new skill set, a new culture and arguably a new sense of identity. This paper is based on research which points to the need to position the learning of literacy and numeracy in the ESL context as a social and educational journey made meaningful by a learner's sense of (emerging) identity.  In this context a holistic, socially orientated  understanding  of  their  learning  and  their progress  is  preferable  to  an approach  which  views  and  evaluates  learners  against  preconceived  functional  literacy skills. The participants in this study were people of refugee background from Africa with minimal literacy skills

Interfaith Dialogue and Comparative Theology: A Theoretical Approach to a Practical Dilemma

Interfaith dialogue is based on the premise that there is more that unites than divides us. Epistemological humility, acceptance of religious plurality or the need for unity itself have all been presented as unifying pathways across disparate religious traditions. Despite such approaches, conceptual understandings of interfaith dialogue have not kept pace with practice. This theoretical paper argues that interfaith dialogical theory profits from a deep understanding of moral psychology and social learning theory. The former posits that a sense of ‘fairness’ and ‘universal care’ are aligned with religious acceptance. On the other hand, values of sanctity, loyalty and authority promote a sense of religious conservatism thereby hindering liberal ideals around plurality and acceptance. The latter suggests that it is first and foremost the exploration of difference, not similarity, which provides the tension to question our preconceived moral values and constructions and thereby move to more inclusive ones. Through contextualising these theories within the reflective spaces at the borders of interfaith dialogue, this paper suggests that bridging difference does not lie in making religious comparisons but rather in accepting religious ambiguity in pursuit of truth. The burgeoning area of comparative theology offers both theoretical and practical guidance for embracing religious diversity in a multi-religious world

Metaphysics and Race

This thesis examines the metaphysics of race. It begins by trying to find an interpretation of the claim that race is socially constructed which makes sense as a position within a substantive metaphysical debate. By identifying the different commitments and controversies in the debate, I argue that the best such interpretation is a constitutive one. I then consider Barnes’s (2020) discussion of the metaphysics of gender, in which she advocates two theses. The negative thesis holds that a successful metaphysics of gender need not line up with ordinary gender terms and beliefs. The positive thesis holds that the metaphysics of gender is concerned with explaining the various phenomena of gender. The expressions required in our ideology and posited categories and entities required in our ontology are those needed to satisfactorily explain gender. In applying this to race, I argue that there is no distinctive explanatory task for metaphysicians of race to engage in. There is no explanatory remainder left once the natural and social sciences have performed their work. The correct metaphysics of race, while concerned with explaining the phenomena of race, is not to be determined by metaphysicians. This is the modified positive thesis. The modified positive thesis fits neatly with the post-Quinean thought that science and metaphysics are continuous. In Chapter 3, I argue for deflationism regarding the actual metaphysics of race debate. There is an ontological consensus - an agreement over what, empirically, there is - between the participants. What they disagree over is what racial concepts (should) apply to. But, while interesting and useful, this isn’t a substantive metaphysical debate. The debate over how to explain race, on the other hand, is substantive. I discuss related issues, including the distinctions between pluralism, deflationism, and racial scepticism, and the presuppositions of the standard debate regarding natural kinds