Partition models for the crystal of the basic $U_q({\widehat{\mathfrak{s}\mathfrak{l}}}_n)$-module

For each $n⩾3$, we construct an uncountable family of models of the crystal of the basic $U_q({\widehat{\mathfrak{s}\mathfrak{l}}}_n)$-module. These models are all based on partitions, and include the usual $n$-regular and $n$-restricted models, as well as Berg’s ladder crystal, as special cases.