Schur Polynomials are families of symmetric polynomials that have been
classically studied in Combinatorics and Algebra alike. They play a central
role in the study of Symmetric functions, in Representation theory [Sta99], in
Schubert calculus [LM10] as well as in Enumerative combinatorics [Gas96, Sta84,
Sta99]. In recent years, they have ... more >>>

We consider arithmetic circuits with arbitrary large (multi-linear) gates for computing multi-linear functions. An adequate complexity measure for such circuits is the maximum between the arity of the gates and their number.
This model and the corresponding complexity measure were introduced by Goldreich and Wigderson (ECCC, TR13-043, 2013), ... more >>>

We show that any Algebraic Branching Program (ABP) computing the polynomial $\sum_{i = 1}^n x_i^n$ has at least $\Omega(n^2)$ vertices. This improves upon the lower bound of $\Omega(n\log n)$, which follows from the classical result of Baur and Strassen [Str73, BS83], and extends the results by Kumar [Kum19], which showed ... more >>>