An illustration of a magnifying glass. An illustration of a magnifying glass.

To go further in understanding the properties of random permutations, we need to use ‘bivariate’ generating functions — that is, generating functions involving 2 variables. Here’s a good introduction ...

Please see exercise 2.8 on page 72 of the textbook. The problem presents three different algorithms for populating an array of size N with a random permutation of the values from 1 through N. Give a ...

Please see exercise 2.8 on page 72 of the textbook. The problem presents three different algorithms for populating an array of size N with a random permutation of the values from 1 through N. Give a ...

Abstract: Given a set of $N$ distinct values, the operation of shuffling those elements and creating a random order is used in a wide range range of applications ...

Quantum spin systems occupy a central role in understanding magnetic phenomena and phase transitions at the microscopic level. In these systems, intrinsic angular momentum (spin) interactions give ...

I want to go back over something from Part 11, but in a more systematic and self-contained way. I’m stating these facts roughly now, to not get bogged down. But I’ll state them precisely, prove them, ...

When permutation methods are used in practice, often a limited number of random permutations are used to decrease the computational burden. However, most theoretical literature assumes that the whole ...

Abstract: The different image block has different sparsity or compressibility in transform domain; in general, the blocks in smooth region have stronger sparsity while those in texture or edge region ...