Under the auspices of the Computational Complexity Foundation (CCF)

REPORTS > KEYWORD > LINEAR FORMS:
Reports tagged with Linear Forms:
TR05-070 | 6th July 2005
Mahdi Cheraghchi

#### On Matrix Rigidity and the Complexity of Linear Forms

The rigidity function of a matrix is defined as the minimum number of its entries that need to be changed in order to reduce the rank of the matrix to below a given parameter. Proving a strong enough lower bound on the rigidity of a matrix implies a nontrivial lower ... more >>>

TR10-181 | 21st November 2010
Hamed Hatami, Shachar Lovett

#### Higher-order Fourier analysis of \$\mathbb{F}_p^n\$ and the complexity of systems of linear forms

In this article we are interested in the density of small linear structures (e.g. arithmetic progressions) in subsets \$A\$ of the group \$\mathbb{F}_p^n\$. It is possible to express these densities as certain analytic averages involving \$1_A\$, the indicator function of \$A\$. In the higher-order Fourier analytic approach, the function \$1_A\$ ... more >>>

ISSN 1433-8092 | Imprint