  A subcategory $\mathscr{W}$ of an abelian category is called wide if it is
closed under kernels, cokernels, and extensions. Wide subcategories are of
interest in representation theory because of their links to other homological
and combinatorial objects, established among others by Ingalls-Thomas and
Marks-\v{S}\v{t}ov\'i\v{c}ek.
  If $d \geqslant 1$ is an integer, then Jasso introduced the notion of
$d$-abelian categories, where kernels, cokernels, and extensions have been
replaced by longer complexes. Wide subcategories can be generalised to this
situation.
  Important examples of $d$-abelian categories arise as the $d$-cluster tilting
subcategories $\mathscr{M}_{n,d}$ of $\operatorname{mod} A_n^{d-1}$, where
$A_n^{d-1}$ is a higher Auslander algebra of type $A$ in the sense of Iyama.
This paper gives a combinatorial description of the wide subcategories of
$\mathscr{M}_{n,d}$ in terms of what we call non-interlacing collections.
