Complexity and asymptotics of structure constants

G Panova - arXiv preprint arXiv:2305.02553, 2023 - arxiv.org
Kostka, Littlewood-Richardson, Kronecker, and plethysm coefficients are fundamental
quantities in algebraic combinatorics, yet many natural questions about them stay …

What is in# P and what is not?

C Ikenmeyer, I Pak - 2022 IEEE 63rd Annual Symposium on …, 2022 - ieeexplore.ieee.org
For several classical nonnegative integer functions we investigate if they are members of the
counting complexity class# P or not. We prove# P membership in surprising cases, and in …

Computational complexity in algebraic combinatorics

G Panova - arXiv preprint arXiv:2306.17511, 2023 - arxiv.org
Algebraic Combinatorics originated in Algebra and Representation Theory, studying their
discrete objects and integral quantities via combinatorial methods which have since …

A remark on the quantum complexity of the Kronecker coefficients

C Ikenmeyer, S Subramanian - arXiv preprint arXiv:2307.02389, 2023 - arxiv.org
We prove that the computation of the Kronecker coefficients of the symmetric group is
contained in the complexity class# BQP. This improves a recent result of Bravyi, Chowdhury …

Positivity of the symmetric group characters is as hard as the polynomial time hierarchy

C Ikenmeyer, I Pak, G Panova - … Mathematics Research Notices, 2024 - academic.oup.com
We prove that deciding the vanishing of the character of the symmetric group is-complete.
We use this hardness result to prove that the absolute value and also the square of the …

On the complexity of evaluating highest weight vectors

M Bläser, J Dörfler, C Ikenmeyer - arXiv preprint arXiv:2002.11594, 2020 - arxiv.org
Geometric complexity theory (GCT) is an approach towards separating algebraic complexity
classes through algebraic geometry and representation theory. Originally Mulmuley and …

Signed combinatorial interpretations in algebraic combinatorics

I Pak, C Robichaux - arXiv preprint arXiv:2406.13902, 2024 - arxiv.org
We prove the existence of signed combinatorial interpretations for several large families of
structure constants. These families include standard bases of symmetric and quasisymmetric …

Algorithms for sparse convolution and sublinear edit distance

N Fischer - 2023 - publikationen.sulb.uni-saarland.de
In this PhD thesis on fine-grained algorithm design and complexity, we investigate output-
sensitive and sublinear-time algorithms for two important problems.(1) Sparse Convolution …

[PDF][PDF] Completeness classes in algebraic complexity theory

P Bürgisser - arXiv preprint arXiv:2406.06217, 2024 - arxiv.org
arXiv:2406.06217v1 [cs.CC] 10 Jun 2024 Page 1 COMPLETENESS CLASSES IN
ALGEBRAIC COMPLEXITY THEORY PETER BÜRGISSER Abstract. The purpose of this …

Equations for GL invariant families of polynomials

P Breiding, R Hodges, C Ikenmeyer… - Vietnam Journal of …, 2022 - Springer
We provide an algorithm that takes as an input a given parametric family of homogeneous
polynomials, which is invariant under the action of the general linear group, and an integer …