Gaps for the Igusa-Todorov function

Abstract For a finite dimensional algebra A, with 0 ϕ dim ( A ) = m ∞ , we show that there always exist modules M and N, such that ϕ ( M ) = 1 , and ϕ ( N ) = m − 1 . On the other hand, we give an example of an algebra such that not every value between 1 and its ϕ-dimension is reached by the ϕ function. We call such values gaps, and show that the algebras with gaps verifies the finitistic dimension conjecture.