|Journal of Integer Sequences, Vol. 22 (2019), Article 19.1.7|
Jeongyoon Choi, Kimyung Kim, and Kyuhyeok Seo
Gyeonggi Science High School for the Gifted
Republic of Korea
We introduce a new set of cards that can be used to count multiplex juggling patterns (when multiple balls can be caught/thrown at a time). This set of cards models the correct behavior and avoids the problems of ambiguity; on the other hand the cards are no longer independent. By use of the transfer matrix method combined with the cards we enumerate multiplex juggling patterns with exactly b balls and hand capacity κ, and include data for κ = 2, 3, and establish some combinatorial properties of the cards.
(Concerned with sequences
Received March 13 2017; revised versions received March 2 2018; January 30 2019; January 31 2019. Published in Journal of Integer Sequences, February 2 2019.