All Questions
16
questions
2
votes
1
answer
42
views
Algorithm to calculate a maximal string from a matrix.
I have stumbled upon an interesting question whilst working on my thesis.
You are given a matrix of pairwise distinct integers $A=(a_{i,j})$ with $1\leq i\leq k$ and $1\leq j \leq r$ and a tuple $(b_1,...
- 175
0
votes
1
answer
52
views
Algorithm for finding maximal "reduction" of an integer matrix
Given a $m\times n$ matrix of non-negative integers. A "reduction" of this matrix can be done on one row/column of this matrix, by subtracting the minimum of the row/column from all other ...
- 96
0
votes
1
answer
55
views
Find exactly k columns in binary matrix such that the sum of those columns is the 1-vector
Suppose I have an $M\times N$ binary matrix where $N$ can be large (say $N\approx10^6$). I want to find exactly $k$ columns ($k$ is relatively small, say $k<10$) such that the sum of those $k$ ...
- 312
2
votes
2
answers
103
views
Finding an algorithm to fill in a matrix subject to conditions
I have a combinatorics problem and I am asking for a solution or a reference in order to solve it.
Since the problem is rather long, I will translate it mathematically.
Suppose I have a $n \times m$ ...
- 1,763
1
vote
1
answer
120
views
Smallest positive integer $M$ in a matrix with given pattern
A square matrix $A$ of $N*N$ contains $-1,1$ only. I can swap any two elements in the array as many times a I want. What is the minimum positive integer $M$ such that $A[i][j]=1$ for all pairs of $(i,...
- 47
-2
votes
2
answers
448
views
Properties of a Matrices whose columns and rows all add to the same value.
Given a matrix A =(aij) that sum of the entries on any row of A is equal to δ and the sum of the entries on any column of A is equal to δ. I was wondering if B=(bij) also has these properties, such ...
- 13
0
votes
1
answer
62
views
Method for optimal de-composition of rank-deficient integer matrices
I'm working with (integer) matrices of reduced rank and try to find a method to decompose the "redundant" columns by some base.
For instance the following matrix $A_5$
...
- 35k
1
vote
3
answers
509
views
Isomorphism of Non-Symmetric Matrices
$A, B$ are non-symmetric matrices of dimension $m \times n$ where $m=n$ or $m \neq n$.
Example: An example of $6 \times 3$ non-symmetric matrix is
$$
\begin{pmatrix}
1 & 0 & 0 \\
0 & ...
- 499
2
votes
0
answers
82
views
Revealed preference rank rule: variation on horse race problem
Suppose there are x number of objects to be ranked. Then there are x[(x-1)/2] possible comparisons of these objects. Only subsets of x can be evaluated for comparisons and there is always one most and ...
- 147
2
votes
0
answers
512
views
How to distribute 5-digit numbers in 5x5 matrices
I have 98000 5-digit numbers, from 00001 to 98000. I need to distribute these 98000 numbers in 14000 5x5 matrices.
A matrix cell must contain only a digit from 0 to 9.
Each matrix must receive 7 ...
- 121
0
votes
0
answers
111
views
Summing the product of combinations of matrix elements
I have a situation where I have an $NxN$ matrix $A$ where each element $a_{i,j}\in\mathbb{R}_{\leq 0}$. I would like to consider the set of all collections of elements such that each collection of $N$ ...
- 121
0
votes
1
answer
398
views
number of ways to fill a 2D grid
We have a 2D grid with n rows and m columns, we can fill it with numbers between 1 and k (both inclusive). Only condition is that for each r such that 1<=r<=k ,no two rows must have exactly the ...
- 315
2
votes
0
answers
651
views
Does a matrix represent a bijection
We have a square binary matrix that represents a connection from rows to columns. Is there a way to tell if a bijection exists (other than checking for all possible bijections and iterating through ...
- 404
3
votes
5
answers
477
views
Translating matrix fibonacci into c++ (how can we determine if a number is fibonacci?)
Is it possible to determine if a number is a fibonacci number in less than N time (where N is the Nth fibonacci number) using the matrix method? I'm trying to exclude external libraries like cmath or ...
- 813
6
votes
1
answer
523
views
Permute the values in each row in a matrix such that the columns sum to the same amount.
The general problem
Given a matrix, I would like to permute the order of values in each row, so that all the columns of the matrix sums to the same value.
A simple example
For example, given:
<...
- 61