All Questions
8 questions
9
votes
2
answers
344
views
Counting $m\times n$ $\bigl({1\atop1}{1\atop0}\bigr)$-free $(0,1)$-matrices
Let $G_{m,n}$ denote the number of $m\times n$ $(0,1)$-matrices that avoid the submatrix $\bigl({1\atop1}{1\atop0}\bigr)$. (Submatrices need not be contiguous.) Here are some small values (not yet on ...
- 667
18
votes
3
answers
8k
views
Number of invertible {0,1} real matrices?
This question is inspired from here, where it was asked what possible determinants an $n \times n$ matrix with entries in {0,1} can have over $\mathbb{R}$.
My question is: how many such matrices ...
- 32.1k
4
votes
1
answer
271
views
The class of $(-1,0,1)$-matrices with all row sums and column sums equal to $0$
Let $n$ be an even positive integer and $W_n$ be the class of all $n\times n$ matrices with entries from the set $\{-1,0,1\}$ such that all row sums and column sums are equal to $0$.
For each $M\in ...
- 32.1k
0
votes
0
answers
299
views
Question on rank of matrices over $\mathbb F_2$
$A$ is a square matrix in $\mathbb F_2^{n\times n}$ of rank $k\leq n-1$.
$B$ is a square matrix in $\mathbb F_2^{n\times n}$ of rank $n$.
$T$ is a square matrix in $\mathbb F_2^{n\times n}$ of rank $1$...
- 13.9k
1
vote
1
answer
60
views
Rank and edges in a combinatorial graph?
Fix a $d\in\mathbb N$ and consider the matrix $M\in\{0,1\}^{2^d\times d}$ of all $0/1$ vectors of length $d$. Consider the matrix $G\in\{0,1\}^{n\times n}$ whose $ij$ the entry is $0$ if inner product ...
- 13.6k
3
votes
0
answers
62
views
How likely is a matrix with exactly $n$ number $1$s per row to avoid a large wide empty submatrix?
Consider the finite collection $M(N,n)$ of all $N \times N$ matrices with exactly $n$ entries per row equal to $1$ and all other entries equal to zero $0$.
By an $a \times b$ submatrix of $M$ we ...
- 1,955
7
votes
1
answer
223
views
Result attribution for eigenvalues of a matrix of Pascal-type
A few years ago, I wanted to cite a result in a paper, for which I could not find a reference. I ended up not using the full strength of it, and the part that I needed could be easily proved. Still, I'...
- 3,255
3
votes
2
answers
543
views
Number of $\{0,1\}$ matrices with distinct rows and distinct columns
How many $M\in\{0,1\}^{r\times c}$ are there such that each row and each column of $M$ is distinct?
How many classes of matrices in $\{0,1\}^{r\times c}$ up to permutation equivalence are there such ...
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