  For the ideal $I = \langle y_1 + \dots + y_n, y^2_1, \dots , y^2_n \rangle$
in $R = {\mathbb F}[y_1, \dots , y_n]$ with char($\mathbb F$) = 0, we show that
the reduced Gr\"obner basis with lex-order consists of polynomials $g_\alpha$
that are represented in terms of paths, moving northeast in the Cartesian
plane, that stay above the diagonal and cross the diagonal at the last step.
This implies that a linear basis for the quotient ring $R/I$ is given by a set
of Catalan paths. We show that the dimension is the number of standard Young
tableaux of size $n$ and height at most two. The graded Frobenius
characteristic of $R/I$ as a symmetric group module is given by
  $\sum_{k=0}^{\lfloor \frac{n}{2} \rfloor } s_{n-k,k}q^k$.
