【报告摘要】Euler showed that the number of partitions of n into distinct parts is equal to the number of partitions of n into odd parts. MacMahon showed that the number of partitions of n for which no part occurs exactly once is equal to the number of partitions of n into parts divisible by 2 or 3. Both these results are instances of a general phenomenon based on the fact that certain polynomials are the product of cyclotomic polynomials. After discussing this assertion, we explain how it can be extended to such topics as counting certain polynomials over finite fields and obtaining Dirichlet series generating functions for certain classes of integers. We also discuss a connection with numerical semigroups.

【报告人简介】Richard P. Stanley现为MIT 应用数学教授。1971年在组合学家Gian-Carlo Rota 指导下获得哈佛大学博士学位。他是国际组合学界的领袖人物之一。其所著两卷本《计数组合学》是该领域的经典，并以此获得2001年度美国数学会的Steele数学论述奖。曾两次在国际数学家大会上作报告(1983年45分钟报告, 2006年1小时报告)。1988年当选美国艺术与科学院院士。1995年，当选美国国家科学院院士。1975年获得美国工业与应用数学会的George Pólya奖。2003年获得Rolf Schock数学奖。