2
votes
1answer
124 views

Ranks of higher incidence matrices of designs

In 1978 Doyen, Hubaut and Vandensavel proved that if $S$ is a Steiner triple system $S(2,3,v)$ then the $GF(2)$ rank of its incidence matrix $N$ is $$ Rk_{2}(N)=v-(d_{p}+1), $$ where $d_{p}$ is the ...
5
votes
0answers
518 views

Status of Hadamard matrix conjecture

I would like to know if any progress has been made on Hadamard conjecture : There exists a Hadamard matrix of order $n=4k$ $\forall k \in \mathbb{N}$.
3
votes
3answers
2k views

What's the maximum determinant of the (0, 1) matrix from M(n, R)?

If there's no exact formula what's the nearest upper and lower bounds do you know?
23
votes
15answers
6k views

Linear Algebra Proofs in Combinatorics?

Simple linear algebra methods are a surprisingly powerful tool to prove combinatorial results. Some examples of combinatorial theorems with linear algebra proofs are the (weak) perfect graph theorem, ...