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Distribution of difference and sum of two permutation matrices

Determinant and permanent of difference and sum of two $n\times n$ permutation matrices can be arbitrarily different.

  1. What is the distribution of determinant of difference and sum and difference of two $n\times n$ permutation matrices?

  2. What is the distribution of permanent of difference and sum and difference of two $n\times n$ permutation matrices?

How much do the distributions differ?

Distribution of difference and sum of permutation matrices

Determinant and permanent of difference and sum of two $n\times n$ permutation matrices can be arbitrarily different.

  1. What is the distribution of determinant of difference and sum of two $n\times n$ permutation matrices?

  2. What is the distribution of permanent of difference and sum of two $n\times n$ permutation matrices?

How much do the distributions differ?

Distribution of sum of two permutation matrices

Determinant and permanent of sum of two $n\times n$ permutation matrices can be arbitrarily different.

  1. What is the distribution of determinant of sum and difference of two $n\times n$ permutation matrices?

  2. What is the distribution of permanent of sum and difference of two $n\times n$ permutation matrices?

How much do the distributions differ?

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Source Link
Turbo
Turbo
  • 13.9k
  • 1
  • 27
  • 76

Distribution of difference and sum of permutation matrices

Determinant and permanent of difference and sum of two $n\times n$ permutation matrices can be arbitrarily different.

  1. What is the distribution of determinant of difference and sum of two $n\times n$ permutation matrices?

  2. What is the distribution of permanent of difference and sum of two $n\times n$ permutation matrices?

How much do the distributions differ?