Asymptotic enumeration of incidence matrices

We discuss the problem of counting {\em incidence matrices}, i.e. zero-one matrices with no zero rows or columns. Using different approaches we give three different proofs for the leading asymptotics for the number of matrices with $n$ ones as $n\to\infty$. We also give refined results for the asymptotic number of $i\times j$ incidence matrices with $n$ ones.Comment: jpconf style files. Presented at the conference "Counting Complexity: An international workshop on statistical mechanics and combinatorics." In celebration of Prof. Tony Guttmann's 60th birthda

Energy conservation and the constitutive relations in chiral and non-reciprocal media

We consider the possibility that the chirality parameters and the non-reciprocity parameters appearing in the constitutive relations for the displacement and magnetic induction fields in a bi-isotropic medium might not be equal and thereby shed light on the physical significance of the fact that they are the same. We find, in particular, that they must be equal in order to retain the local conservation of energy

Reply to comment on `Energy conservation and the constitutive relations in chiral and non-reciprocal media'

We respond to the comment by Mackay and Lakhtakia on our paper. These authors have missed the simple point that our chirality and non-reciprocity parameters are real. The 'inconsistency' claimed by them emerges from their incorrect attempt to apply our results instead to complex chirality and non-reciprocity parameters