Combinatorics Undergraduate Research Seminar (FGCU-CUReS)
In 2018, Drs. Katie Johnson, Shaun Sullivan, and I formed the Combinatorics Undergraduate Research Seminar (FGCU-CUReS) to share our favorite mathematical theories and problems with FGCU students.
Fall 2021
This semester we will start by introducing a combinatorial problem posed by Dr. Shaun Sullivan motivated by the many terrible drivers in Southwest Florida.
A Merging Problem Posed by Dr. Shaun Sullivan
This paper was a result of the seminar that fall
https://arxiv.org/abs/2203.02501
Time permitting we will also discuss how to count tetras tilings of the plane following methods introduced to us by Dr. Steve Butler.
Spring 2021 - Student Presentations
Florida Undergraduate Research Conference (FURC) March 26, 2021:
Tipsy Cops and Robbers on Graphs - Viktoriya Bardenova and Vincent Ciarcia
Tipsy Cops and Robbers: The Modeling of Pursuit Scenarios on Various Graphs - Peter Phan
A Merging Problem Posed by Dr. Shaun Sullivan
Publications
Markov Models for the tipsy cop and robber game on graphs (Viktoriya Bardenova and Vincent Ciarcia)
Here are some combinatorics conferences or workshops that have gone online this year.
Spring 2020 - Lecture Notes on Umbral Calculus - led by Shaun Sullivan
FGCU Community Engagement & Research Day (CERD 2020)Domination Theory and the Placement of Solar Panels - Viktoriya Bardenova
Alyson Baumgardner, Brooklyn Crum
Morgan Bettencourt, Andrew Mckay, Carlton Saunderson
The Mathematics of Gerrymandering - Meghan Carlson
Collin Garofalo
Thuan Huynh
Joshua Teeter
Tom Shlomi
Lars Nilsen
Here are some papers with CUReS students.
Fall 2019 Lecture Notes on Coxeter Groups - led by Erik Insko
Lecture 1 - Why study Coxeter groups? Slides
Lecture 2 - Presenting Coxeter groups. Slides
Lecture 3 - Using technology to develop conjectures. Slides Calculations
Lecture 4 - A "Cayley-esque" theorem and brainstorming approaches to the ADL conjecture. Slides
Lecture 5 - A combinatorial approach to root systems. Slides Calculations Webpage with calculations
Lecture 6 - Inversion sets, Bruhat order, and a new conjecture involving pinnacle sets of permutations Slides
Lecture 7 - More on Bruhat Order, Counting using "q-analogues", and some proofs our Conjectures! Slides
Diaz-Lopez's Peak Set Palindromicity Conjecture that we explored in this seminar was recently resolved by Gaetz and Gao. See their preprint for elegant proofs of the palindromicity result and more open problems.
A formula for enumerating permutations with a fixed pinnacle set - this is joint work with Alexander Diaz-Lopez, Pamela Harris, Isabella Huang, and Lars Nilsen.
Spring 2019 Lecture Notes on Ramsey Theory - led by Dr. Katie Johnson
Fall 2018 Lecture Notes on Generating Functions - led by Dr. Shaun Sullivan
