Sortable Simplicial Complexes and $t$-Independence Ideals of Proper Interval Graphs

  • Jürgen Herzog
  • Fahimeh Khosh-Ahang
  • Somayeh Moradi
  • Masoomeh Rahimbeigi


We introduce the notion of sortability and $t$-sortability for a simplicial complex and study the graphs for which their independence complexes are either sortable or $t$-sortable. We show that the proper interval graphs are precisely the graphs whose independence complex is sortable. By using this characterization, we show that the ideal generated by all squarefree monomials corresponding to independent sets of vertices of $G$ of size $t$ (for a given positive integer $t$) has the strong persistence property, when $G$ is a proper interval graph. Moreover, all of its powers have linear quotients.

Article Number