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**Lara Pudwell**, Rutgers University, lpudwell {at} math [dot] rutgers [dot] edu**Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: On subholonomic functions

Speaker: **Marko Petkovsek**, University of Ljubljana (Ljubljana, Slovenia).

Date: Thursday, May 1, 2008 5:00pm

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

Abstract:

Substantial progress has been made in the past in design of algorithms for the class of holonomic functions, which has very nice closure properties. Although large, this class still fails to include several important and relatively simple functions, encountered in combinatorial enumeration, such as ordinary powers, Stirling numbers of first and second kind, and Eulerian numbers. So it seems necessary to turn attention to ``subholonomic functions'' which retain some, but not all of the nice properties of holonomic functions. The hope is that this may help us in tackling certain easy-to-state but difficult-to-solve combinatorial problems, such as enumeration of lattice paths in restricted regions, and enumeration of permutations avoiding a forbidden pattern.