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MIT PRIMES/Art of Problem Solving

CROWDMATH 2023: Arithmetic of Power Monoids

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Welcome to CrowdMath 2023!
felixgotti   7
N Aug 13, 2023 by felixgotti
Hi everyone!

Welcome to CrowdMath 2023!

CrowdMath is a collaborative and inclusive research program welcoming participants from all cultural background and region in the planet. With this in mind, we expect all participants to be respectful with their peers and mentors.

Research Project

Our research project this year will be focused on additive combinatorics and power monoids. We will initially consider certain open questions related the set of all finite subsets consisting of nonnegative integers under the Minkowski addition (see https://en.wikipedia.org/wiki/Minkowski_addition). Following our motivating paper (see https://arxiv.org/abs/1701.09152), we call this the power monoid of $\mathbb{N}_0$. Then keeping Minkowski addition in mind, we will study generalized versions of the power monoid of $\mathbb{N}_0$. Although the algebraic (ideal theoretical) and arithemetic properties of power monoids have been systematically investigated only recently, there has been a significant activity in this research area during the last five years. This last statement will be ratified by the CrowdMath resources we will be posting throughout the next few months.

Problems

The section Problems contains the main open problems pertaining the CrowdMath 2023 project. The problems will become systematically available during the coming months as we progress and learn the necessary background and tools needed to understand and work on them. All of the proposed open problems will be thematically linked to the 2023 CrowdMath research project. Most of the problems in the section Problems will have an associated resource, which can be found in the section Resource.

Resources

The content of each resource is directly connected and relevant to the CrowdMath 2023 project. Indeed, each resource contains the notions, definitions, and tools the participants will be learning as the primary sources to understand and make progress on the coming list of open problems. Resources also comes with practice exercises for participants to train. We highly encourage CrowdMath participants to try to solve all the practice exercises, as this will help to deeper understand the new concepts and to get a better insight of the overall project. Participants can discuss the exercises by clicking either the `View Discussions' or `Start New Topic' button.

Intellectual Property

As CrowdMath is a massive collaborative project, sometimes it is not possible to determine the lines between one participant's work and the rest of the group. In such cases, the results created must be attributed to all CrowdMath contributors.
7 replies
felixgotti
Jan 26, 2023
felixgotti
Aug 13, 2023
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