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Expansion Formulae in the Algebra of Shuffles
Student-Run Research 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.