# Math 583: COMBINATORICS II Spring 2003 (Rutgers University) Webpage

http://sites.math.rutgers.edu/~zeilberg/math583.html

Last Update: June 2, 2003.

TEXT: Handouts

• Teacher: Dr. Doron ZEILBERGER ("Dr. Z")
• Classroom: Thursdays: Hill 525; Mondays: "smart" classrom ARC bldg (inside computer lab).
• Time: Mondays and Thursdays , period 2 (9:50-11:10am)
• Dr. Zeilberger's Office: Hill Center 704 ( Phone: (732) 445-1326)
• Dr. Zeilberger's E-mail: zeilberg@math.rutgers.edu
• Dr. Zeilberger's Office Hours: MTh 9:00-9:30 am, and by appointment

## AIM

This Course is Self-Contained, and no prerequisite is needed, in particular, Math 582 (Combinatorics I) is NOT a prerequisite! This semester we will focus on the exciting subject of Algebraic Combinatorics (tableaux, permutations, Schur and Jack polynomials). We will emphasize the algorithmic and constructive aspects. We will also approach the subject from the viewpoint of my other great love: Experimental Mathematics, and will use Maple to explore it. No knowledge of Maple is assumed, and at the end of the semester you will not only be proficient in algebraic combinatorics, but you will also be a Maple whiz, over and above using it as a fancy symbolic calculator.

## The package SF

While learning Maple and Symmetric Functions, we will, together, construct some Maple packages. So far we have SF and RSK. At the end of the semester, instead of an exam, students will add to it by implementing an advanced topic.

Here are the Current Version of SF, and the Current Version of RSK.

• David Biddulph's RRS program is part of the above-mentioned RSK, (type "Help(RRS);").
• JDT, written by Rohan Fernandes.
• FranzblauZeilberger, written by Roman Holowinsky, implementing the celebrated bijective proof of Debbie Franzblau and Doron Zeilberger.
• LLL, written by Mohamud Mohammed, implementing the even more famous Lenstra-Lenstra-Lovasz algorithm.
• NPS, written by Vince Vatter, implementing the Novelli-Pak-Stoyanovski algorithm for the proof of the hook-lengths formula.

## Suggested Final Projects

Individual suggestions for Final Project
Added Jan. 23, 2012: Congratulations to Roman Holowinsky, who was a student in this class, for winning the 2011 prestigious Ramanujan SASTRA prize! .
Doron Zeilberger's teaching page