This paper produces a recursive formula of the Betti numbers of certain StanleyReisner ideals (graph ideals associated to forests). This gives a purely combinatorial definition of the projective dimension of these ideals, which turns out to be a new numerical invariant of forests. Finally, we propose a possible extension of this invariant to general graphs. 0. Introduction Throughout this paper...

In this survey, we discuss two research areas related to Massey’s higher operations. The first direction is connected with the cohomology of Lie algebras and theory representations. second main theme at intersection toric topology, homotopy polyhedral products, homology local rings, Stanley–Reisner rings simplicial complexes.

We study binary linear codes C obtained from the quadric Veronese embedding of P3 in P9 over F2. show how one can find higher weight spectra these codes. Our method will be a Stanley-Reisner rings series matroids associated to each code C.