Partial Algebraic Shifting

Computing the algebraic shift of a uniform hypergraph or a simplicial complex is resource intensive. We discuss improvements to the general algorithm for computations over the exterior algebra that lead to the definition of partial algebraic shifting. Further, we provide a sufficient condition for a partial algebraic shift to preserve the Betti numbers in terms of the weak order. This talk is based on joint work with Michael Joswig and Fabian Lenzen.