arXiv subjects

D. W. Morris

Publications and source records attributed to D. W. Morris.

2 recordsLinked to original sources

arXiv2026

Bounded elementary generation of SL_2: nearly the end

Let $\mathcal{O}_S$ be the ring of $S$-integers of a global field $K$ of any characteristic, where $S$ is a finite set of valuations of $K$ (and $S$ contains all of the archimedean valuations if the characteristic is zero). We prove that if $|S| \ge 2$, then every unimodular $(2 \times 2)$-matrix over $\mathcal{O}_S$ is a product of $\leq 7$ elementary matrices. This nearly optimal bound essentially concludes the investigation of bounded elementary generation of $SL_2(\mathcal{O}_S)$ started over 50 years ago.

math.GR↗

arXiv2011

Hamiltonian cycles in Cayley graphs whose order has few prime factors

We prove that if Cay(G;S) is a connected Cayley graph with n vertices, and the prime factorization of n is very small, then Cay(G;S) has a hamiltonian cycle. More precisely, if p, q, and r are distinct primes, then n can be of the form kp with k < 32 and k not equal to 24, or of the form kpq with k < 6, or of the form pqr, or of the form kp^2 with k < 5, or of the form kp^3 with k < 3.

math.CO↗