create a matrix with specific conditions - c

Question

I would like to create a matrix with these specifics
text of exercise
write a program that reads a number k > 0 and a permutation of the first K numbers (from 0 to k-1) that does not fix any element and produce (printing on consecutive lines) permutations p0, . . . , ph such that (1) p0 is permutation given in input; (2) fro every i > 0, pi is the smallest permutation of K cthat does not fix any element and does not collide with any other permutation from p0 and pi−1. We say that 2 permutations p1, p2 ok
K collides if exists and index i from 1 to k such that p1(i) = p2(i).
my ideas i wanted to create a k*k matrix amd the first row will be the imput of a vector i will declare. I tought to fill the matrix in these way : let's take a specific element v[i][j]
v[i][j]is in the matrix if 1)v[k][j] from k =0,...,i-1 is different from v[i][j],1)v[i][k] from k =0,...,i-1 is different from v[i][j],v[i][j] is different from i , and from the remaining possibilities for v[i][j] it is the minimum from the remainin number 0,...k-1
code implementations
#include <stdio.h>
#include <stdlib.h>
#define N 50
typedef int matrix[N][N];
int min(int vector[],int n)
{
int i;
int p=0;
int min=vector[0];
for(i=0; i<n;i++)
{
if (vector[i]<=min)
{
min=vector[i];
p=i;
}
}
return min;
}
int main()
{
int k;
printf("\n insert a number ");
scanf("%d",&k);
int v[k][k];//creation of matrix I wanted
int input[k];//first row
int arrayindex[k]={0};// array from 0 to k
for(int u=0; u<k;u++)
{
arrayindex[u]=u;
}
printf("insert component of vector:");
for(int l=0;l<k;l++)
{
printf("input[%d]= ",l);
scanf("%d",&input[l]);
}
//print vector
for(int l=0;l<k;l++)
{
printf("%d",input[l]);
}
printf("\n\n");
// copy first row
for(int j=0;j<k;j++)
{
v[0][j]=input[j];
}
//printf of first row
for(int j=0;j<k;j++)
{
printf("\nv[0][%d]=%d ",j,v[0][j]);
}
//try to fill matrix
for(int i=1; i<k;i++)
{
for(int j=0;j<k;j++)
{
if (j=0){
v[i][j]!=v[i-1][j];
v[i][j]!=j;
v[i][j]=min(arrayindex,k);}
if(j!=0)
v[i][j]!=v[i-1][j];
v[i][j]!=v[i][j-1];
v[i][j]!=j;
v[i][j]=min(arrayindex,k);
}
}
//print of matrix
printf("\n the matrix is:\n ");
for(int i=0; i<k;i++)
{ printf("\n");
for(int j=0;j<k;j++)
{
printf("%d",v[i][j]);
}
}
return 0;
}
the problem in this code is in the section called try to fill matrix . When I compile nothing appear on the screen .Where is the problem ? is at least idea correct?