Enumerating indices of Schubert varieties defined by inclusions

By extending the notion of grid classes to include infinite grids, we establish a structural characterisation of the simple permutations in Av(4231,35142,42513,351624)$\mathrm{Av}(4231,35142,42513,351624)$, a pattern class which has three different connections with algebraic geometry, including the specification of indices of Schubert varieties defined by inclusions. This characterisation leads to the enumeration of the class.