Juggling and applications to q-analogues

Excedances of affine permutations

“…We will study these coset representatives by considering their associated juggling sequences. We refer the reader to the papers [6,8,9] and the book [14] for more on the mathematics of juggling. Here we give a brief introduction.…”

“…A crossing is two directed edges i → j and k → such that i < k < j < ; see [9]. The number of crossings cross(a) of a juggling sequence a is the number of crossings such that 1 i n. This extra condition implies that number of crossings is finite and we are not counting crossings that are equivalent by a shift of a multiple of the period n.…”

“…1. Note that these juggling cards are the mirror images of the cards introduced in [9]. As in [9] by taking n juggling cards C *…”

“…An earlier combinatorial proof was given by Ehrenborg and Readdy [9] using juggling sequences. In this paper we will refine the Ehrenborg-Readdy juggling approach to give a proof of the length distribution of the coset representatives of the parabolic subgroup.…”

Universal juggling cycles

“…The sequences, often called \site-swaps", have been investigated from a variety of perspectives [1,2,3,6,9] and lead to many interesting mathematical questions (as well as some killer juggling patterns! ).…”