M. Grannell

collaborators

2 papers

math.CO2018

Embedding partial Latin squares in Latin squares with many mutually orthogonal mates

Diane M. Donovan, Mike Grannell, Emine Şule Yazıcı

We show that any partial Latin square of order $n$ can be embedded in a Latin square of order at most $16 n^{2}$ which has at least $2 n$ mutually orthogonal mates. We also show that f…

math.CO2017

Enumerations of maximum partial triple systems on 16 and 17 points

Fatih Demirkale, Diane Donovan, Mike Grannell

For $v \equiv 1$ or 3 (mod 6), maximum partial triple systems on $v$ points are Steiner triple systems, STS( $v$ )s. The 80 non-isomorphic STS(15)s were first enumerated around 100 ye…