All Questions
Tagged with nonnegative-matrices co.combinatorics
7 questions
1
vote
0
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83
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Weird transportation polytope
I'm looking to compute extremal points of a weird polytope. This polytope contains all matrices with positive entries $A \in \mathcal M_{n,m}\left(\mathbb R_+\right)$ such that:
every row sum except ...
- 686
1
vote
0
answers
88
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On the real and finite field rank of a $0/1$ matrix - II
Let $M\in\{-\ell,\dots,-1,0,+1,\dots,+\ell\}^{n\times n}$ be a matrix of rank $r$ where $\ell\geq1$ such that there is a permutation matrix in $\{0,1\}^{m\times m}$ of order $2\ell$.
Fix a permutation ...
- 13.9k
4
votes
1
answer
317
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On the real and finite field rank of a $0/1$ matrix - I
Let $M\in\{-1,0,+1\}^{n\times n}$ be a matrix of rank $r$.
Consider the matrix $f(M)\in\{0,+1\}^{mn\times mn}$ where $0$ in $M$ is replaced by $m\times m$ all $0$ matrix, $+1$ in $M$ is replaced by $m\...
- 13.9k
3
votes
2
answers
543
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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 ...
user94040
2
votes
0
answers
115
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Polynomials with positive coefficients passing through fixed points/range of Vandermonde matrices
I'll give two equivalent statements of the setup, then give my questions.
Fix integers $M \leq N$ and define the Vandermonde-like matrix $V_{M,N}[i,j] = (1 - \frac{i}{M})^{j-1}$ for $i \in \{1,2,\...
- 21
6
votes
2
answers
2k
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Extreme points of transportation polytope
I'm interested in $n \times m$ joint probability tables with prescribed row and column marginals. Such tables form a convex set known as the transportation polytope. What are the extreme points of ...
- 291
22
votes
3
answers
2k
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Sampling from the Birkhoff polytope
The set of $n\times n$ real, nonnegative matrices whose rows and columns sum to one forms the well-known Birkhoff polytope
Recently someone asked me if I knew
How to sample (in polynomial time) ...
- 28.6k