  In the 40s, Mayer introduced a construction of (simplicial) $p$-complex by
using the unsigned boundary map and taking coefficients of chains modulo $p$.
We look at such a $p$-complex associated to an $(n-1)$-simplex; in which case,
this is also a $p$-complex of representations of the symmetric group of rank
$n$ - specifically, of permutation modules associated to two-row compositions.
In this article, we calculate the so-called slash homology - a homology theory
introduced by Khovanov and Qi - of such a $p$-complex. We show that every
non-trivial slash homology group appears as an irreducible representation
associated to two-row partitions, and how this calculation leads to a basis of
these irreducible representations given by the so-called $p$-standard tableaux.
