Mathematics Colloquia and Seminars
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Expansion Formulae for Top to Random ShufflingStudent-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.