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Computing all binary matrices with given row and column sum
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Given $a,b in mathbbN$, and $r,c in mathbbN$. I want to
construct all matrices $A in 0,1^a times b$ such that each row of $A$
contains exactly $r$ ones and each column of $A$ contains exactly $c$ ones. Generally $a neq b$ and $r neq c$.
If it makes constructing these matrices $A$ any simpler, one can also assume that each row and column in $Acdot A^T$ appears the same number of times.
My first thought was that one can set the first row and column of $A$ without loss of generality and then compute all possible permutations of the first row and column and combine them together. Most of the time this does not yield a matrix with the desired properties because one does not use the information about the rows and column simultaneously.
Does anyone have any ideas? One can further assume that $a+b leq 30$ holds.
combinatorics matrices
asked Jul 16 at 15:41
Dominik B.
887
add a comment |Â
up vote
2
down vote
favorite
Given $a,b in mathbbN$, and $r,c in mathbbN$. I want to
construct all matrices $A in 0,1^a times b$ such that each row of $A$
contains exactly $r$ ones and each column of $A$ contains exactly $c$ ones. Generally $a neq b$ and $r neq c$.
If it makes constructing these matrices $A$ any simpler, one can also assume that each row and column in $Acdot A^T$ appears the same number of times.
My first thought was that one can set the first row and column of $A$ without loss of generality and then compute all possible permutations of the first row and column and combine them together. Most of the time this does not yield a matrix with the desired properties because one does not use the information about the rows and column simultaneously.
Does anyone have any ideas? One can further assume that $a+b leq 30$ holds.
combinatorics matrices
asked Jul 16 at 15:41
Dominik B.
887
add a comment |Â
up vote
2
down vote
favorite
up vote
2
down vote
favorite
Given $a,b in mathbbN$, and $r,c in mathbbN$. I want to
construct all matrices $A in 0,1^a times b$ such that each row of $A$
contains exactly $r$ ones and each column of $A$ contains exactly $c$ ones. Generally $a neq b$ and $r neq c$.
If it makes constructing these matrices $A$ any simpler, one can also assume that each row and column in $Acdot A^T$ appears the same number of times.
My first thought was that one can set the first row and column of $A$ without loss of generality and then compute all possible permutations of the first row and column and combine them together. Most of the time this does not yield a matrix with the desired properties because one does not use the information about the rows and column simultaneously.
Does anyone have any ideas? One can further assume that $a+b leq 30$ holds.
combinatorics matrices
asked Jul 16 at 15:41
Dominik B.
887
Given $a,b in mathbbN$, and $r,c in mathbbN$. I want to
construct all matrices $A in 0,1^a times b$ such that each row of $A$
contains exactly $r$ ones and each column of $A$ contains exactly $c$ ones. Generally $a neq b$ and $r neq c$.
If it makes constructing these matrices $A$ any simpler, one can also assume that each row and column in $Acdot A^T$ appears the same number of times.
My first thought was that one can set the first row and column of $A$ without loss of generality and then compute all possible permutations of the first row and column and combine them together. Most of the time this does not yield a matrix with the desired properties because one does not use the information about the rows and column simultaneously.
Does anyone have any ideas? One can further assume that $a+b leq 30$ holds.
combinatorics matrices
asked Jul 16 at 15:41
Dominik B.
887
asked Jul 16 at 15:41
Dominik B.
887
asked Jul 16 at 15:41
Dominik B.
887
asked Jul 16 at 15:41
Dominik B.
887
887
add a comment |Â
add a comment |Â
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