Research Initiation Award: Turan-type problems on partially ordered sets

研究启动奖：偏序集上的图兰型问题

• 批准号: 2247163
• 负责人: Shanise Walker
• 金额: $ 29.99万
• 依托单位: Clark Atlanta University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-08-01 至 2026-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2247163&HistoricalAwards=false
• 关键词: Research; Initiation; Award; Turan; type

HBCU-UP’s Research Initiation Awards provide support for STEM faculty to pursue research activities to further their research capabilities and effectiveness and help enhance research and teaching at HBCUs. This award to Clark Atlanta University (CAU) will establish a research program in combinatorics aimed at advancing the study of partially ordered sets and structures that do not contain them. This project will further enrich teaching and learning at CAU by engaging underrepresented minority undergraduate students in experiential learning through research training and opportunities to enhance their skill sets while preparing them for advanced degrees or to enter the workforce in STEM fields.The goal of this project is to conduct research on Turán-type problems and expand the knowledge of Turán-type theory on partially ordered sets (posets). Posets are sets which are reflexive, antisymmetric, and transitive. Turán-type poset problems investigate the maximum size of a family in the 𝑛-dimensional Boolean lattice poset that does not contain some subposet, which is called the forbidden subposet problem. Specifically, this project aims to resolve the forbidden subposet problem on posets like the crown poset, and advance the forbidden subposet problem and the poset saturation problem for induced subposets. This project will utilize programming code in Python to analyze the structural properties of families in the Boolean lattice that do not contain various posets. The analyses will then be used to improve currently known techniques like counting and discharging arguments to solve the forbidden subposet and poset saturation problems for various (induced) subposets. The findings of this project will significantly advance the knowledge and study of Turán-type theory for posets and induced posets. In collaboration with Carnegie Mellon University, the proposed project will integrate the learning of combinatorics foundations, programming in Python, and research in combinatorics for underrepresented minority undergraduate students at Clark Atlanta University.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

HBCU-UP的研究启动奖为STEM教师提供了购买研究活动的支持，以进一步提高其研究能力和有效性，并有助于增强HBCUS的研究和教学。授予克拉克亚特兰大大学（CAU）的奖项将建立一项研究计划，旨在推进对不包含它们的部分有序的集合和结构的研究。该项目将通过研究培训和机会来提高他们的技能，同时为高级学位做好准备，或者在STEM领域中进入劳动力，这将进一步丰富CAU的教学和学习。 POSET是反射性，反对称和及时效果的集合。研究不包含某些子插入的𝑛维布尔晶格poset中家族的最大大小，这称为禁止子插入问题。具体而言，该项目旨在解决诸如皇冠poset之类的POSET上的禁止子pose问题，并推进禁止的子pose问题和诱导子poset的Poset饱和问题。该项目将利用Python中的编程代码来分析布尔晶格中不包含各种posets的家庭的结构属性。然后，这些分析将用于改善当前已知的技术，例如计数和排放参数，以解决各种（诱导）子焦点的禁止子框和Poset饱和问题。该项目的发现将大大提高Turán类型理论的POSET和POSET的知识和研究。在与卡内基·梅隆大学（Carnegie Mellon University）的合作中，该提议的项目将整合组合基础的学习，Python的编程以及针对Clark Atlanta University的代表性不足的少数族裔本科生的组合学研究。这项奖项反映了NSF的法定任务，并通过评估了基金会的概念，以表现出对基金会的支持。