First written: March 22, 2026
This version: April 6, 2026
The class should be partitioned into teams of one, two (optimally), or three students.
Students should pick a project no later then 8:00 pm, April 5, 2026 (it should be included in the homework due that day). But the membeship is first-come-first-serve, so you are welcome to email me as soon as you decide, in order to guarantee a place.
-YOU ARE WELCOME TO PROPOSE A PROJECT NOT LISTED BELOW-
The team leader will be in charge of coordinating the various contributions, and writing up (with the team's help) explaining it
The projects should be ready by: Wed., May 6, 2026, 8:00pm emailed to ShaloshBEkhad@gmail.com. Each project-leader should email TWO attachments: projX.txt and projX.pdf where 1 ≤ X ≤ 4
The student presentation will take place, via WebEx, on May 7, 2026, 9:30-10:50 am (WebEx invitation will be sent by May 5)
Part I (formerly Project 1)
Using the preliminary Maple package (that you should expand) DZtools.txt, try to get as many sequences as possible for enumerating the number of lattice walks from the origin to [n,...,n] using a symmetric set of steps. Find which ones are already in the OEIS, and for new ones, enter at least some of them to the OEIS.
Also (for the OEIS) find the asymptotic expressions for the sequences using procedures Asy and/or AsyC in the Maple package
AsyRec.txt
(type ezra(Asy) and ezra(AsyC) for instructions)
Part II (formerly the original project 2)
Using the preliminary Maple package (that you should expand) DZtools.txt, try to get as many sequences as possible for enumerating the number of lattice walks from the origin back to the origin in n steps using a symmetric set of steps and their reverses. Find which ones are already in the OEIS, and for new ones, enter at least some of them to the OEIS.
Also (for the OEIS) find the asymptotic expressions for the sequences using procedures Asy and/or AsyC in the Maple package
AsyRec.txt
(type ezra(Asy) and ezra(AsyC) for instructions)
Project Leader: Caroline Cote
Other team member: Guy Adami
Study the Statistics of Standard Young tableau using the Greene-Nijenhuis-Wilf amazing algorithm (to be covered in class soon). Incorporate methods from statistics, including Bradley Efron's Bootstrap method
Project Leader: Aurora Hiveley
Other team member: Lucy Martinez
Experiment with the Robinson-Schenstead algorithm, combining it with the Bootstrap method to find statistical properties of permutations reflected by the RS algorithm.
Project Leader: Austin DeCicco
Other team members:Jike Liu
Experiment with generalizations of Conway's John Conway's Subprime Fibonacci sequences.
Project Leader Abrar Almahmeed
Other team member: Pablo Blanco