All Questions
5
questions
55
votes
21
answers
14k
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, ...
10
votes
4
answers
5k
views
Maximum determinant of $\{0,1\}$-valued $n\times n$-matrices
What's the maximum determinant of $\{0,1\}$ matrices in $M(n,\mathbb{R})$?
If there's no exact formula what are the nearest upper and lower bounds do you know?
- 101
3
votes
1
answer
408
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 ...
- 6,832
3
votes
1
answer
125
views
On the half-skew-centrosymmetric Hadamard matrices
Definition 1: A Hadamard matrix is an $n\times n$ matrix $H$ whose entries are either $1$ or $-1$ and whose rows are mutually orthogonal.
Definition 2: A matrix $A$ is half-skew-centrosymmetric if ...
- 264
3
votes
0
answers
132
views
Linear combinations of special matrices
I am a hobby computer scientist and I have a problem to which I am searching an efficient algorithm.
Given an integer n, we want to combine some square input-matrices of size n in a way that is ...
- 73