Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:****Andrew Baxter**, Rutgers University, baxter{at} math [dot] rutgers [dot] edu**Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: In How Many Ways Can you Break up Many Russian Dolls?

Speaker: **Doron Zeilberger**, Rutgers University

Date: Thursday, September 10, 2009 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

If you only have one Russian Doll (Matryoshka), this is a Stirling question, and it rings a Bell (as Joel Spencer put it (private communication), ca. 1981). But if you have k identical such babushkas, then things become much more complicated. The case k=2 is in Sloane, and goes back to Comtet (1968), but k=3 and beyond is missing, and apparently the "formulas" previously suggested in the literature were too complicated to implement. Thotsaporn "Aek" Thanatipanonda and I found a (relatively) quick way to compute many terms for k=3,4,5, ...., by teaching the computer how to automatically generate the "evolution differential operator" (all by itself), and then using it to crank out as many terms as desired.