RTG: Combinatorics, Computation, and Applications at Iowa State University

RTG：爱荷华州立大学的组合学、计算和应用

• 批准号: 1839918
• 负责人: Leslie Hogben
• 金额: $ 150万
• 依托单位: Iowa State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-05-01 至 2025-02-28
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1839918&HistoricalAwards=false
• 关键词: RTG; Combinatorics; Computation; Applications; Iowa

The mathematical field of combinatorics and graph theory studies patterns of relationships between objects, and has applications throughout the mathematical, physical, biological, and social sciences and engineering. This makes it an ideal area in which to train interdisciplinary scientists with strong computational skills. This Research Training Group (RTG) in Combinatorics, Computation, and Applications builds on and expands the Iowa State University Mathematics Department's nationally recognized work in recruitment, retention, graduation and placement of groups underrepresented in mathematics; the RTG faculty team provides mathematical role models for women, minorities, and veterans. This program will use computation, experimentation, and applications to facilitate the transition from student to research mathematician, using teams of undergraduate students, graduate students, postdoctoral researchers and faculty to prepare junior personnel for successful careers in academia or industry. Research projects in Combinatorics in Algebra and Geometry, Extremal and Probabilistic Combinatorics, and Applied Combinatorics will foster a bidirectional flow of ideas between combinatorics and applications. A rotation model will be adapted from the bench sciences to provide broad training for both graduate and undergraduate students on a variety of different topics through the use of research teams; leadership of the teams will be provided by postdoctoral associates. The RTG will collaborate with the Graduate Research Workshop in Combinatorics (GRWC), with RTG trainees participating and the establishment of a pre-GRWC mini-course providing training in tools of computational combinatorics. Mentoring is a key component: the RTG faculty will mentor all participants and postdoctoral associates and graduate students will mentor those junior to themselves.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.

组合数学和图论的数学领域研究对象之间的关系模式，并在整个数学，物理，生物和社会科学和工程中应用。 这使得它成为培养具有强大计算能力的跨学科科学家的理想领域。这个研究培训小组（RTG）在组合学，计算和应用的基础上，并扩大了爱荷华州州立大学数学系在招聘，保留，毕业和安置数学代表性不足的群体的国家认可的工作; RTG教师团队为妇女，少数民族和退伍军人提供数学榜样。该计划将使用计算，实验和应用程序，以促进从学生到研究数学家的过渡，使用本科生，研究生，博士后研究人员和教师团队为学术界或工业界的成功职业生涯准备初级人员。在代数和几何组合学，极值和概率组合学，应用组合学的研究项目将促进组合学和应用之间的思想的双向流动。 轮换模式将适应从板凳科学提供广泛的培训研究生和本科生在各种不同的主题，通过使用研究团队;团队的领导将由博士后助理提供。 RTG将与组合学研究生研究讲习班（GRWC）合作，RTG受训人员参加并建立一个GRWC前迷你课程，提供计算组合学工具的培训。指导是一个关键组成部分：RTG教师将指导所有参与者，博士后助理和研究生将指导那些比他们年轻的人。这个奖项反映了NSF的法定使命，并被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

项目成果

The maximum number of 10- and 12-cycles in a planar graph

平面图中 10 圈和 12 圈的最大数量

• DOI: 10.1016/j.disc.2022.113245
• 发表时间: 2023
• 期刊: Discrete Mathematics
• 影响因子: 0.8
• 作者: Cox, Christopher;Martin, Ryan R.
• 通讯作者: Martin, Ryan R.

On the edit distance function of the random graph

关于随机图的编辑距离函数

• DOI: 10.1017/s0963548321000353
• 发表时间: 2022
• 期刊: Probability and Computing
• 作者: Martin, Ryan R.;Riasanovsky, Alex W.
• 通讯作者: Riasanovsky, Alex W.

A Family of Convex Sets in the Plane Satisfying the (4, 3)-Property can be Pierced by Nine Points

平面上满足 (4, 3) 性质的凸集族可以被九点贯穿

• DOI: 10.1007/s00454-022-00391-y
• 发表时间: 2022
• 期刊: Discrete & Computational Geometry
• 影响因子: 0.8
• 作者: McGinnis, Daniel

New upper bounds for the Erdős-Gyárfás problem on generalized Ramsey numbers

广义 Ramsey 数的 ErdÅs-Gyårfás 问题的新上限

• DOI: 10.1017/s0963548322000293
• 发表时间: 2023
• 期刊: Probability and Computing
• 作者: Cameron, Alex;Heath, Emily
• 通讯作者: Heath, Emily

Isomorphisms and Properties of TAR Graphs for Zero Forcing and Other X-set Parameters

迫零和其他 X 集参数的 TAR 图的同构和性质

• DOI: 10.1007/s00373-023-02677-1
• 发表时间: 2023
• 期刊: Graphs and Combinatorics
• 影响因子: 0.7
• 作者: Bong, Novi H.;Carlson, Joshua;Curtis, Bryan;Haas, Ruth;Hogben, Leslie
• 通讯作者: Hogben, Leslie