We consider the ring S = C[xij ] of polynomial functions on the vector space C m×n of complex m × n matrices. We let GL = GLm(C) × GLn(C) and consider its action via row and column operations on C m×n (and the induced action on S). For every GL-invariant ideal I ⊆ S and every j ≥ 0, we describe the decomposition of the modules ExtjS(S/I, S) into irreducible GL-representations. For any inclusion...

We study powers of binomial edge ideals associated with closed and block graphs.

The symbolic powers, in general, are not equal to the ordinary powers. Therefore, one interesting question here is for what classes of ideals and powers coincide? answer this square-free monomial may be packing property. In paper, we classify all cubic path those coincide.

We investigate ideals in a polynomial ring which are generated by powers of linear forms. Such ideals are closely related to the theories of fat point ideals, Cox rings, and box splines. We pay special attention to a family of power ideals that arises naturally from a hyperplane arrangement A. We prove that their Hilbert series are determined by the combinatorics of A, and can be computed from ...