Question

3. For a deck consisting of 32 playing cards, let A denote the riffle shuffle which interleaves the top half of the deck with the bottom half, but keeps the top and bottom cards fixed Similarly let B denote the other kind of riffle (in which all cards move). (a) Write out the permutations, of the 32 positions in the deck, represented by these riffles A and B. Give each as a product of cycles b) How many different rearrangements of the deck are possible, using just the A riffle? (c) How many different rearrangements of the deck are possible, using the B riffle! d) For a full deck of 52 cards, write out the permutations representing the A and B shuffles Answer questions (b) and (c) for these shuffles of the 52-card deck.

Answer 1

Solution:

Given that

A denote the riffle shuffle which interleaves the top half of the deck with the bottom half,but keeps the top and bottom cards fixed.

B denote the other kind of riffle( in which all cards move)

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