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Expansion Formulae for Top to Random Shuffling

Student-Run Applied & Math Seminar

Speaker: Roger Tian, UC Davis
Location: 2112 MSB
Start time: Wed, Oct 29 2014, 12:10PM

Card shuffling is a much-studied topic in probability theory and combinatorics. In the top to random shuffle, the first a cards are removed from a deck of n cards 12 ... n and then inserted back into the deck. I will analyze top to random shuffling from a combinatorial perspective, by deriving an expansion formula for these shuffles via a bijection and further generalizing the formula to the situation where each card in the deck has multiple faces. These expansion formulae can be used for enumeration and calculating probabilities.