Y by TheMath_boy, PiGuy3141592, antoinelab01, DapperPeppermint, cw357, Bradygho
This year, our main topic is extremal combinatorics, with a focus on problems about sequences and 0-1 matrices. These problems have applications to many areas including:
-robot navigation (e.g. an algorithm for finding a shortest path between two given points in a grid with obstacles)
-discrete geometry (e.g. an upper bound on the maximum number of unit distances in a convex n-gon), and
-permutation pattern avoidance (the solution to the Stanley-Wilf conjecture).
Researchers have been investigating these kinds of problems for over fifty years. The topic requires no background knowledge besides basic combinatorics. You can learn more about relevant definitions and background reading on the Resources page. That page has a list of papers and exercises with each paper. All of the exercises are solved problems, they are there to help understand the topic.
The Problems page has a list of open problems. These problems are unsolved, most are from publications, and I made some of them. I’ll post some more open problems later in the year, and typically crowdmath participants also suggest open problems. Here are some examples of Crowdmath research papers from past years:
https://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i1p5
https://arxiv.org/search/math?searchtype=author&query=CrowdMath%2C+P+A
https://arxiv.org/abs/2008.13302
https://arxiv.org/abs/1710.11352
-robot navigation (e.g. an algorithm for finding a shortest path between two given points in a grid with obstacles)
-discrete geometry (e.g. an upper bound on the maximum number of unit distances in a convex n-gon), and
-permutation pattern avoidance (the solution to the Stanley-Wilf conjecture).
Researchers have been investigating these kinds of problems for over fifty years. The topic requires no background knowledge besides basic combinatorics. You can learn more about relevant definitions and background reading on the Resources page. That page has a list of papers and exercises with each paper. All of the exercises are solved problems, they are there to help understand the topic.
The Problems page has a list of open problems. These problems are unsolved, most are from publications, and I made some of them. I’ll post some more open problems later in the year, and typically crowdmath participants also suggest open problems. Here are some examples of Crowdmath research papers from past years:
https://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i1p5
https://arxiv.org/search/math?searchtype=author&query=CrowdMath%2C+P+A
https://arxiv.org/abs/2008.13302
https://arxiv.org/abs/1710.11352