Homological Invariants Of Squarefree Powers Of Simplicial Trees

In this thesis, we study the squarefree powers of facet ideals associated with simplicialtrees. Specifically, we examine the linearity of their minimal free resolution andtheir regularity. Additionally, we investigate when the first syzygy module of squarefreepowers of facet ideal of a simplicial tree is generated by linear relations. Finally,we provide a combinatorial formula for the regularity of the squarefree powers oft-path ideals of path graphs.