n this work we intro duce a new set of invariants asso ciated to the linear strands of a minimal free resolution of a Z -graded ideal I R = | [ x 1 ;:::;x n ] . We also prove that these invariants satisfy some prop erties analogous to those of Lyub eznik numb ers of lo cal rings. In particular, they satisfy a consecutiveness prop erty that we prove rst for Lyub eznik numb ers. For the case of squarefree monomial ideals we get more insight on the relation b etween Lyub eznik numb ers and the linear strands of their asso ciated Alexander dual ideals. Finally, we prove that Lyub eznik numb ers of Stanley- Reisner rings are not only an algebraic invariant but also a top ological invariant, meaning that they dep end on the homeomorphic class of the geometric realization of the asso ciated simplicial complex and the characteristic of the base field