Conference matrices and unimodular lattices

Conference matrices are used to define complex structures on real vector spaces. Certain lattices in these spaces become modules for rings of quadratic integers. Multiplication of these lattices by non-principal ideals yields simple constructions of further lattices including the Leech lattice.Comment: 17 pages. Subitted to European Journal of Combinatoric

Combinatorial proofs of q-series identities

We provide combinatorial proofs of some of the q-series identities considered by Andrews, Jimenez-Urroz and Ono [q-series identities and values of certain $L$-functions. Duke Math. J. 108 (2001), no. 3, 395--419].Comment: 14 pages. Submitted to Journal of Combinatorial Theory

Alternating sign matrices and tournaments

We settle a question of Bressoud concerning the existence of an explicit bijection from a class of oriented square-ice graphs to a class of tournaments. We give an algorithm constructing such a bijection.Comment: 18 pages, LaTeX; minor corrections. To appear in FoataFest proceedings issue of Advances in Applied Mathematic

Symmetric Pascal matrices modulo p

We study characteristic polynomials of symmetric matrices with entries ${i+j\choose i}$ the binomial coefficients, over finite fields.Comment: 16 pages, added reference, changes in presentation, correction of an error in a proo

Two closed forms for the Bernoulli polynomials

In the paper, the authors find two closed forms involving the Stirling numbers of the second kind and in terms of a determinant of combinatorial numbers for the Bernoulli polynomials and numbers.Comment: 7 page

Content without context is noise : Looking for curriculum harmony in primary arts education in Western Australia

Arts education in Western Australian primary schools consist of learning opportunities outlined by mandated curriculum. However, assumptions underlying this curriculum involving access, resources and support impact schools’ capacity to implement the curriculum without them being adequately addressed by the written curriculum. Drawing on the policy enactment theory of Ball, Maguire, and Braun (2012), four contextual variables (situated contexts, professional cultures, material contexts and external factors) are used to highlight the differences between the written published curriculum and the implemented, practised curriculum. Drawing on interviews with 24 participants across four schools issues of geographic location, use of arts specialists, appropriate learning spaces and the stresses associated with mandated literacy and numeracy testing are reported as contextual pressures by this study. This paper details the disruptive interference of these contextual pressures that we describe as ‘noise’. The provision of a better understanding of this contextual landscape brings schools and teachers away from the ‘noise’ of disruption and closer to curriculum harmony