** Speaker:** Steve Butler, Iowa State University

** Title:** Enumerating (multiplex) juggling patterns with cards

** Abstract: **
A main problem in the mathematics of juggling is enumerating the number of juggling patterns with
given constraints. The most beautiful method for counting all patterns where we only catch/throw at
most one ball at a time is through the use of cards introduced by Ehrenborg and Readdy. When we are
allowed to catch/throw more than one ball at a time (multiplex juggling) the problem is more
difficult. We will show that by modifying the cards that we can count multiplex juggling patterns;
these cards also appear to have some unusual combinatorial properties which would make their study
interesting in their own right.