This paper initiates a systematic development of a theory of non-commutative optimization, a
setting which greatly extends ordinary (Euclidean) convex optimization. It aims to unify and …

We present a polynomial time algorithm to approximately scale tensors of any format to
arbitrary prescribed marginals (whenever possible). This unifies and generalizes a …

We show that the problem of deciding positivity of Kronecker coefficients is NP-hard.
Previously, this problem was conjectured to be in P, just as for the Littlewood–Richardson …

The permanent versus determinant conjecture is a major problem in complexity theory that is
equivalent to the separation of the complexity classes $\mathrm {VP} _ {\mathrm {ws}} $ and …

A bstract We show that the counting of observables and correlators for a 3-index tensor
model are organized by the structure of a family of permutation centralizer algebras. These …

Quantum teleportation is one of the fundamental building blocks of quantum Shannon
theory. While ordinary teleportation is simple and efficient, port-based teleportation (PBT) …

Kostka, Littlewood-Richardson, Kronecker, and plethysm coefficients are fundamental
quantities in algebraic combinatorics, yet many natural questions about them stay …

Kostka, Littlewood-Richardson, Plethysm and Kronecker coefficients are the multiplicities of
irreducible representations in decomposition of representations of the symmetric group that …

Given a random quantum state of multiple distinguishable or indistinguishable particles, we
provide an effective method, rooted in symplectic geometry, to compute the joint probability …

Algebraic Combinatorics originated in Algebra and Representation Theory, studying their
discrete objects and integral quantities via combinatorial methods which have since …