Mathematical Sciences: Undergraduate Research in Graph Theory and Number Theory

数学科学：图论和数论本科研究

• 批准号: 9200329
• 负责人: Clifford Reiter
• 金额: $ 0.7万
• 依托单位: Lafayette College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-06-01 至 1993-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9200329&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Undergraduate; Research; Graph

This award supports two undergraduate researchers working under the supervision of the principal investigator on problems in two areas of mathematics. In the first, number theory, the students will consider convergents of continued fractions reduced by an integer, with special attention paid to cases involving very small periods. Work will also be done in graph theory. Here the research will focus on polynomial invariants: distinguishing graphs by Tutte polynomials and unimodality of Whitney numbers. If the schedule permits, studies of network reliability will also be conducted.

该奖项支持两名本科生研究人员在首席研究员的指导下研究两个数学领域的问题。在第一个数论中，学生将考虑被整数化简的连分式的收敛性，并特别注意涉及非常小周期的情况。图论方面的工作也会做。这里的研究将集中在多项式不变量：通过Tutte多项式和Whitney数的单模性来区分图。如果时间表允许，还将进行网络可靠性研究。