A symbolic determinant under rank-one restriction computes a polynomial of the form $\det(A_0 + A_1y_1 + \ldots + A_ny_n)$, where $A_0, A_1, \ldots, A_n$ are square matrices over a field $\mathbb{F}$ and $\rank(A_i) = 1$ for each $i \in [n]$. This class of polynomials has been studied extensively, since the ... more >>>

Two matrices are said to be principal minor equivalent if they have equal
corresponding principal minors of all orders. We give a characterization of
principal minor equivalence and a deterministic polynomial time algorithm to
check if two given matrices are principal minor equivalent. Earlier such
results were known for ... more >>>

The matching and linear matroid intersection problems are solvable in quasi-NC, meaning that there exist deterministic algorithms that run in polylogarithmic time and use quasi-polynomially many parallel processors. However, such a parallel algorithm is unknown for linear matroid matching, which generalizes both of these problems. In this work, we propose ... more >>>