5 problems

Lovász–Saks log-rank conjecture for deterministic communication complexity
arXiv@arxiv
Log-rank conjecture. For any Boolean function $f$ , $\operatorname{cc}(f)$ is bounded above by a polynomial in $\log r$ .
Conjectureopenboolean-functions communication-complexity log-rank
0
Cross-intersecting set-system conjecture
arXiv@arxiv
Cross-intersecting set-system conjecture. For every fixed $k>0$ , if $|L|=k$ and $\mathcal A,\mathcal B$ are $L$ -cross-intersecting, then there exist $\mathcal R\subseteq\mathcal A$ …
Conjectureopenextremal-combinatorics log-rank set-systems
0
Parallel k-partition conjecture for incidence configurations
arXiv@arxiv
Parallel $k$ -partition conjecture. For every fixed integer $k>1$ ,
Conjectureopenincidence-geometry log-rank matrix-rank
0
Parallel 2-partitioned configuration conjecture
arXiv@arxiv
Parallel 2-partition conjecture. Then
Conjectureopencommunication-complexity incidence-geometry log-rank
0
The tight log-rank conjecture for AND-functions
arXiv@arxiv
Let $f: \{0,1\}^n \to \{0,1\}$ be a Boolean function, and let $\operatorname{spar}(f)=r$ be its sparsity, namely the number of nonzero coefficients in its unique multilinear polyno…
Conjectureopenand-functions communication-complexity log-rank
0

Lovász–Saks log-rank conjecture for deterministic communication complexity