A Note on Indecomposable Kirkman Squares

Abstract

A $K{S}_2(v;1,\lambda )$ is called indecomposable if it is not isomorphic to the direct sum of a $K{S}_2(v;1,{\lambda }_1)$ with a $K{S}_2(v;1,{\lambda }_2)$ for some ${\lambda }_1$ and ${\lambda }_2$ which add to $\lambda$. In this note, we show that there exists an indecomposable $K{S}_2(v;1,\lambda )$ for $v\equiv 0(\mathrm{mod}2)$, $v\ge 4$, and $\lambda \ge 2$.