What combinatorics principles model complex scenarios like favored rank clumping in deterministic key shuffles?

[Killman2002]

Combinatorics principles that can model complex scenarios like favored rank clumping in deterministic key shuffles include:

1. Multinomial distribution: Multinomial distribution can model the probabilities of various combinations of cards occurring within a deterministic key shuffle, including the formation of favored rank clumps.

2. Markov chains: Markov chains can model the transition probabilities of cards moving through the shuffle process, allowing for the analysis of how rank clumping might develop over time.

 

[CR7]

Another combinatorial principle that can be used to model complex scenarios like favored rank clumping in deterministic key shuffles is generating functions. Generating functions can help represent the distribution of cards within a deck and analyze the probabilities of specific card patterns or rank clumps emerging during the shuffle process. By manipulating generating functions, one can derive equations to calculate the probabilities of certain outcomes occurring, including the formation of favored rank clumps. This approach provides a powerful tool for understanding and quantifying the phenomenon of rank clumping in deterministic key shuffles.