Seminar Details
Algebraic generating functions
- Start Date: November 2, 2026
- End Date: November 2, 2026
- Event Start Time: 2:00 PM
- Event End Time: 3:00 PM
- Event Location: Conference Room 705 | Rutgers University | Hill Center | 110 Frelinghuysen Rd
- Seminar Type: Current Seminars
- Seminar Series: Rutgers Discrete Mathematics Seminar
- Presenter(s): Robin Pemantle, UPenn
- Presentation Type: Stand Alone Presentation
- Abstract:
There is by now a well known theory of asymptotic estimation when a multivariate array has a rational generating function. After a brief recap, I will treat this as a black box and examine the problem of coefficient estimation when the multivariate generating function is algebraic. Algorithmically, one may solve the "algebraic connection problem" along branches, reducing the estimation problem in many cases to known harmonic analysis.
To illustrate these methods in a combinatorial setting, I will discuss the univariate toy example of Catalan numbers, and then present examples of multivariate combinatorial enumeration: assembly trees, bi-colored Motzkin paths, and 0-2-5 trees.