M. Grannell

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20172026

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math.CO2026

On the minimum number of entries in a pair of maximal orthogonal partial Latin squares

Diane M. Donovan, Mike Grannell, Emine Şule Yazıcı

It is shown that if $F$ denotes the number of filled cells in a superimposed pair of maximal orthogonal partial Latin squares of order $n$ , then $F \geq n^{2} /3$ . This resolves a conje…

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…