Combinatorics-related Open Problems Seminar (CROPS)
An online seminar for presentation of open problems with combinatorial flavor. This includes problems within the field of Mathematics, Theoretical Computer Science, Statistics, etc.
Each of the talks at the CROP seminar aims to lead to new collaborations and obtaining of new results.
Organizers: Stoyan Dimitrov (emailТoStoyan {at} gmail.com),
Sam Spiro (sas703 {at} scarletmail.rutgers.edu)
Why present at CROPS? Do you have an exciting problem related to Combinatorics? Do you want to find other people to think about it? Don't wait until the next big conference!
Contact the organizers and send an abstract to present your problem at CROPS.
Why attend CROPS? Are you looking for new projects, ideas, collaborators, or do you just want to hear about some interesting problems in Combinatorics? If so, you should attend our meetings!
Format, Mailing List and Time:
Format: The total duration of each talk (including questions) is not more than 30 minutes. Most of the talks are 10 to 20 minutes with a few minutes for questions at the end.
Each attendee can reach out to the presenter after the talk and the presenter can form a working group with all interested people. A useful resource here might be
this file on supercollaboration.
Join our mailing list:
Subscribe here. You will receive only one email two days prior to each talk.
Time: Usually, we meet bi-weekly on Friday, 12:15pm (Eastern Time, i.e., New York time).
Schedule SPRING SEMESTER 2023:
Talk 7:
Date: Friday, Feb 17, 2023, 12:15pm (Eastern Time, i.e., New York time)
Zoom Link:
https://rutgers.zoom.us/j/98270180477?pwd=VkpsRkg2ZWo4cDU5MTk0bFpzaENSZz09
Passcode: 112515
Speaker: Benjamin Przybocki, Stanford University
Title: Delicate and k-delicate words [
link to slides]
Abstract: We study words that barely avoid repetitions, for a couple of senses of "barely". Three kinds of repetition are squares, cubes and overlaps. A square (respectively, cube) is a word of the form XX (respectively, XXX), where X is a nonempty word. An overlap is a word of the form xYxYx, where x is a letter and Y is a possibly empty word. We say a word is squarefree (respectively, cubefree, overlap-free) if none of its factors is a square (respectively, cube or overlap), and in addition such a word is called delicate if changing any one of its letters creates a square (respectively cube or overlap). We classify the lengths of delicate squarefree, overlap-free, and cubefree words over binary and ternary alphabets. Then, we introduce a generalization of delicacy and raise a question about it for further study.
Talk 8:
Date: Friday, March 3, 2023, 12:15pm (Eastern Time, i.e., New York time)
Zoom Link:
https://rutgers.zoom.us/j/98270180477?pwd=VkpsRkg2ZWo4cDU5MTk0bFpzaENSZz09
Passcode: 112515
Speaker: Sam Spiro, Rutgers University
Title: Another Open Problems Collection
Abstract: In grad school I started maintaining a small list of open problems of interest on my website. In this talk we'll go through the list and highlight some of my personal favorite problems.
Talk 9:
Date: Friday, March 24, 2023, 12:15pm (Eastern Time, i.e., New York time)
Zoom Link:
https://rutgers.zoom.us/j/98270180477?pwd=VkpsRkg2ZWo4cDU5MTk0bFpzaENSZz09
Passcode: 112515
Speaker: Miroslav Marinov, Oxford University (recent graduate)
Title: Pointsets with angles of bounded magnitude [
link to slides]
Abstract: Given a real number $\alpha \in [\pi/3, \pi)$ and an integer $d\geq 2$, what is the maximum possible size of a set of points in $\mathbb{R}^d$, such that any angle formed by three of them has size less than or equal to $\alpha$? We shall outline results and connections to combinatorial problems about hypergraphs in some of the regimes for $\alpha$, such as: $\alpha$ close to $\pi/3$ (almost equilateral triangle sets), $\alpha = \pi/2$ (acute sets) and $\alpha$ close to $\pi$ (very obtuse sets). It is also interesting to think about the rate of growth of the maximum size as $\alpha$ increases.
Talk 10:
Date: Friday, April 7, 2023, 12:15pm (Eastern Time, i.e., New York time)
Zoom Link:
https://rutgers.zoom.us/j/98270180477?pwd=VkpsRkg2ZWo4cDU5MTk0bFpzaENSZz09
Passcode: 112515
Speaker: Luz Elena Grisales Gómez, MIT (recent graduate)
Title: BFS vs DFS for a random target in plane trees [
link to slides]
Abstract: Assume that we are at the root of a random plane tree with n nodes which is not known to us. Our goal is to find a target node and we choose to use either BFS or DFS at the beginning. We investigate the question which of the two algorithms is a better choice for different values of the level of the target node? A few related question will be also proposed.