Journal of Combinatorics
Volume 8 (2017)
Guest Editor: Steve Butler (Iowa State University)
Juggling card sequences
Pages: 507 – 539
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.
juggling, cards, crossings, enumeration
2010 Mathematics Subject Classification
Steve Butler is partially supported by an NSA Young Investigator Grant.
Paper received on 21 June 2015.