  I conjecture three identities for the determinant of adjacency matrices of
graphene triangles and trapezia with Bloch (and more general) boundary
conditions. For triangles, the parametric determinant is equal to the
characteristic polynomial of the symmetric Pascal matrix. For trapezia it is
equal to the determinant of a sub-matrix. Finally, the determinant of the tight
binding matrix equals its permanent. The conjectures are supported by analytic
evaluations and Mathematica, for moderate sizes. They establish connections
with counting problems of partitions, lozenge tilings of hexagons, dense loops
on a cylinder.
