1 citations · 2 across the 10 of their papers we have counts for
15 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, Harry Hylock, Matthew C. Lettington +1
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…
Multifactorisations and Divisor Functions
Ambrose D. Law, Matthew C. Lettington, Karl Michael Schmidt
We consider a joint ordered multifactorisation for a given positive integer into parts, where , and each part is split into one…
Integer matrix factorisations, superalgebras and the quadratic form obstruction
Nicholas J. Higham, Matthew C. Lettington, Karl Michael Schmidt
We identify and analyse obstructions to factorisation of integer matrices into products or of matrices with rational or integer entries. The obstructions arise as qua…
Divisor Functions and the Number of Sum Systems
Matthew C. Lettington, Karl Michael Schmidt
Divisor functions have attracted the attention of number theorists from Dirichlet to the present day. Here we consider associated divisor functions which for non-neg…
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 the Structure of Additive Systems of Integers
M. N. Huxley, M. C. Lettington, K. M. Schmidt
A sum-and-distance system is a collection of finite sets of integers such that the sums and differences formed by taking one element from each set generate a prescribed arithmetic…
Binomial Polynomials mimicking Riemann's Zeta Function
Mark W. Coffey, Matthew C. Lettington
The (generalised) Mellin transforms of certain Chebyshev and Gegenbauer functions based upon the Chebyshev and Gegenbauer polynomials, have polynomial factors , whose zeros…
On Block Representations and Spectral Properties of Semimagic Square Matrices
S. L. Hill, M. C. Lettington, K. M. Schmidt
Using the decomposition of semimagic squares into the associated and balanced symmetry types as a motivation, we introduce an equivalent representation in terms of block-structured…
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…
On Fibonacci Polynomial Expressions for Sums of th Powers, their implications for Faulhaber's Formula and some Theorems of Fermat
M. W. Coffey, M. C. Lettington
Denote by the sum of the -th powers of the first positive integers . Similarly let be the -fold sum of the -th powers of the firs…
On Higher Dimensional Fibonacci Numbers, Chebyshev Polynomials and Sequences of Vector Convergents
Mark W. Coffey, James L. Hindmarsh, Matthew C. Lettington +1
We study higher-dimensional interlacing Fibonacci sequences, generated via both Chebyshev type functions and -dimensional recurrence relations. For each integer , there exist…
Mellin transforms with only critical zeros: Chebyshev and Gegenbauer functions
Mark W. Coffey, Matthew C. Lettington
We consider the Mellin transforms of certain Chebyshev functions based upon the Chebyshev polynomials. We show that the transforms have polynomial factors whose zeros lie all on th…
Mellin transforms with only critical zeros: Legendre functions
Mark W. Coffey, Matthew C. Lettington
We consider the Mellin transforms of certain Legendre functions based upon the ordinary and associated Legendre polynomials. We show that the transforms have polynomial factors who…
A trio of Bernoulli relations, their implications for the Ramanujan polynomials and the zeta constants
Matthew C. Lettington
We study the interplay between recurrences for zeta related functions at integer values, `Minor Corner Lattice' Toeplitz determinants and integer composition based sums. Our invest…