We provide formulas for the degrees of the projections of the locus of square matrices with given rank from linear spaces spanned by a choice of matrix entries. The motivation for these computations stem from applications to ‘matrix rigidity’; we also view them as an excellent source of examples to test methods in intersection theory, particularly computations of Segre classes. Our results are ...

The dependence of the Dewar resonance energy (DRE) on the Kekulé structure count (K) was found to be significantly different from that earlier anticipated. Within classes of benzenoid isomers, the DRE increases either as K for 0.3 or as (ln K) for 2. Both functional dependencies result in approximate expressions for DRE of nearly equal accuracy. Approximations of the form DRE a K + b and DRE a'...

In the class of isomeric linearly annelated derivatives of coronene, the species with greatest number of Kekulé structures is determined.

We point out that the zero-energy Landau level of Dirac fermions in graphene can be, in the presence of a repulsive electronelectron interaction, split into two associated with a “bond ordering” formation having a “Kekulé pattern”, which respects the chiral symmetry. Since the Kekulé pattern has a three-fold degeneracy, domain structures are implied, for which we show that in-gap states localiz...

Organic molecules characterized by high-spin ground states are of interest for many reasons, including their potential use as spin reservoirs in ferromagnetic organic materials. For the design of high-spin organic molecules having an even number of electrons, one typically tries to take advantage of Hund’s rule 4 in constructing systems biased towards having triplet ground states. That is, one ...