Juggling card sequences
Combinatorics
2015-04-08 v1
Abstract
Juggling patterns can be described by a sequence of cards which keep track of the relative order of the balls at each step. This interpretation has many algebraic and combinatorial properties, with connections to Stirling numbers, Dyck paths, Narayana numbers, boson normal ordering, arc-labeled digraphs, and more. Some of these connections are investigated with a particular focus on enumerating juggling patterns satisfying certain ordering constraints, including where the number of crossings is fixed.
Cite
@article{arxiv.1504.01426,
title = {Juggling card sequences},
author = {Steve Butler and Fan Chung and Jay Cummings and Ron Graham},
journal= {arXiv preprint arXiv:1504.01426},
year = {2015}
}
Comments
29 pages