# Permanent versus determinant, obstructions, and Kronecker coefficients

@inproceedings{Burgisser2015PermanentVD, title={Permanent versus determinant, obstructions, and Kronecker coefficients}, author={Peter Burgisser}, year={2015} }

We give an introduction to some of the recent ideas that go under the name “geometric complexity theory”. We first sketch the proof of the known upper and lower bounds for the determinantal complexity of the permanent. We then introduce the concept of a representation theoretic obstruction, which has close links to algebraic combinatorics, and we explain some of the insights gained so far. In particular, we address very recent insights on the complexity of testing the positivity of Kronecker…

## 8 Citations

Rectangular Kronecker Coefficients and Plethysms in Geometric Complexity Theory

- Mathematics2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)
- 2016

It is proved that the vanishing of rectangular Kronecker coefficients cannot be used to prove superpolynomial lower bounds on dc(perm), the determinantal complexity of the permanent polynomial.

No Occurrence Obstructions in Geometric Complexity Theory

- Mathematics2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)
- 2016

The permanent versus determinant conjecture is a major problem in complexity theory that is equivalent to the separation of the complexity classes VP ws and VNP and it is proved that the approach to separating these orbit closures by exhibiting occurrence obstructions is impossible.

A Determinantal Identity for the Permanent of a Rank 2 Matrix

- Mathematics
- 2019

We prove an identity relating the permanent of a rank 2 matrix and the determinants of its Hadamard powers. When viewed in the right way, the resulting formula looks strikingly similar to an identity…

On the largest Kronecker and Littlewood-Richardson coefficients

- MathematicsJ. Comb. Theory, Ser. A
- 2019

No occurrence obstructions in geometric complexity theory

- MathematicsJournal of the American Mathematical Society
- 2018

The permanent versus determinant conjecture is a major problem in complexity theory that is equivalent to the separation of the complexity classes
V
P
w
s
\mathrm…

The Computational Complexity of Plethysm Coefficients

- MathematicsComput. Complex.
- 2020

This work is the first to apply techniques from discrete tomography to the study of plethysm coefficients and derive new lower and upper bounds and in special cases even combinatorial descriptions for plethYSm coefficients, which the authors consider to be of independent interest.

POLYNOMIAL-TIME PLAINTEXT-RECOVERY ATTACK ON THE MATRIX-BASED KNAPSACK CIPHER

- Computer Science, Mathematics
- 2020

The aim of the present paper is to propose a polynomial-time plaintext-recovery attack on the matrix-based knapsack cipher, a novel additively homomorphic asymmetric encryption scheme that can be considered broken and should not be used as a privacy tool.

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The permanent versus determinant conjecture is a major problem in complexity theory that is equivalent to the separation of the complexity classes VP ws and VNP and it is proved that the approach to separating these orbit closures by exhibiting occurrence obstructions is impossible.

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