6 papers
Enumerating Hamiltonian Paths and Cycles
Harry Hylock, Karl Michael Schmidt, Matthew C. Lettington
We prove counting formulae for the number of directed Hamiltonian paths and directed Hamiltonian cycles in any complete multipartite graph. The method is based on a collapsing tech…
On c-polynomial factorisations
Harry G. Hylock, Matthew C. Lettington, Karl Michael Schmidt
c-Polynomials are polynomials whose (non-zero) coefficients are all equal to 1. Taking a theorem by Carlitz and Moser as a motivation, we prove a structure theorem for the factoris…
On the resolvent convergence of discrete Dirac operators on 3D cubic lattices
Karl Michael Schmidt, Tomio Umeda
We prove that the discrete Dirac operators in three dimensions converge to the continuum Dirac operators in the strong resolvent sense, but not in the norm resolvent sense.
Some Properties and Applications of Non-trivial Divisor Functions
S. L. Hill, M. N. Huxley, M. C. Lettington +1
The th divisor function , which counts the ordered factorisations of a positive integer into positive integer factors, is a very well-known arithmetic function; in part…
On Superalgebras of Matrices with Symmetry Properties
S. L. Hill, M. C. Lettington, K. M. Schmidt
It is known that semi-magic square matrices form a 2-graded algebra or superalgebra with the even and odd subspaces under centre-point reflection symmetry as the two components. We…
Exceptional coupling constants for the Coulomb-Dirac operator with anomalous magnetic moment
K. M. Schmidt
It was recently shown that the point spectrum of the separated Coulomb-Dirac operator H_0(k) is the limit of the point spectrum of the Dirac operator with anomalous magnetic moment…