A Bijection between Shuffles and Set Partitions
نویسنده
چکیده
Recall from Garsia’s paper that Ba is the group algebra Q(Sn) element Ba = 1 2 3 · · · a Wa,n = ∑ α∈Sa α Wa,n, where Wa,n is the word Wa,n = (a+ 1)(a+ 2) · · ·n. The motivation is that we have a deck of cards labelled 1, 2, . . . , n, and Ba represents all possible decks that may result from removing the cards 1, 2, . . . , a and then inserting them back into the deck (consisting of the cards a + 1, a + 2, . . . , n). Each of these resulting decks can be viewed as a permutation in Sn, described more precisely in the following. Such a resulting deck u = c1c2 · · · cn (where ci ∈ [n]) can be viewed as the permu-
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