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Expansion Formulae in the Algebra of Shuffles

Student-Run Applied & Math Seminar

Speaker: Roger Tian, UC Davis
Location: 2112 MSB
Start time: Mon, Dec 3 2012, 12:10PM

I will talk about a certain set of elements B_a (where a is an integer between 1 and n) of the algebra generated by S_n over the rationals. These elements correspond to certain ways of shuffling a deck of n cards. Expansion formulae for some of these elements have been derived in previous papers by Persi Diaconis, Adriano Garsia, and others. I will present a bijective proof of one of these formulas, which I discovered earlier this year. Then I will mention various open problems in relation to these shuffling elements.