The Spectrum of Self-converse $MTS$

Abstract

A Mendelsohn triple system, $MTS(v)=(X,\mathcal{B})$, is called self-converse if it and its converse $(X,{\mathcal{B}}^{-1})$ are isomorphic, where ${\mathcal{B}}^{-1}=\{⟨z,y,x⟩;⟨x,y,z⟩\in \mathcal{B}\}$. In this paper, the existence spectrum of self-converse $MTS(v)$ is given, which is $v\equiv 0$ or $1(\mathrm{mod}3)$ and $v\ne 6$.