Open Access
Multivariate juggling probabilities
Arvind Ayyer,Jérémie Bouttier,Sylvie Corteel,François Nunzi +3 more
- 16 Jun 2014
pp 1-12
TL;DR: In this paper, the authors considered refined versions of Markov chains related to juggling and showed that the stationary distribution can be obtained in finite time in one case, where the normalization factor is closed-form.
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Abstract: We consider refined versions of Markov chains related to juggling. We further generalize the construction to juggling with arbitrary heights as well as infinitely many balls, which are expressed more succinctly in terms of Markov chains on integer partitions. In all cases, we give explicit product formulas for the stationary probabilities and closed-form expressions for the normalization factor. We also refine and generalize enriched Markov chains on set partitions. Lastly, we prove that in one case, the stationary distribution is attained in finite time.
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Citations
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References
Nonequilibrium statistical mechanics of the zero-range process and related models
Martin R. Evans,T Hanney +1 more
TL;DR: In this article, the authors review recent progress on the zero-range process, a model of interacting particles which hop between the sites of a lattice with rates that depend on the occupancy of the departure site.
A maj Statistic for Set Partitions
TL;DR: A weighting of set partitions which is analogous to the major index for permutations, and the corresponding weight generating function yields the q-Stirling numbers of the second kind of Carlitz and Gould.
62
Enumerating (Multiplex) Juggling Sequences
Steve Butler,Ron Graham +1 more
TL;DR: In this paper, the problem of enumerating periodic σ-juggling sequences of length n for multiplex juggling, where σ is the initial state (or landing schedule) of the balls, was studied.