理学院学术报告:Statistics on Integer Partitions
发布时间: 2018-11-07  浏览次数: 10

理学院报告题目: Statistics on Integer Partitions

报告人:    臧经涛博士

报告人单位:哈尔滨工业大学

报告日期:20181108

报告时间:下午1500—1600

报告地点:江宁校区励学楼B 219

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摘要:Let spt(n) denote the total number of appearances of the smallest parts in all the partitions of $n$. The spt-crank of a vector partition was introduced by Andrews, Garvan and Liang which leads to combinatorial interpretations of the congruences of spt(n) mod 5 and 7. Andrews, Dyson and Rhoades proposed the problem of finding a definition of the spt-crank for ordinary partitions. In this talk,we introduce the structure of doubly marked partitions and establish a bijection between ordinary partition and doubly marked partition, which can be used to divide the set of partitions counted by spt(5n+4) (or spt(7n+5)) into five (or seven) equinumerous classes. We also answer the conjecture also raised by Andrews, Dyson and Rhoades on the unimodality of spt-crank. Moreover, we will discuss the unimodality of the crank on ordinary partitions, which answers the conjecture raised by Chan and Mao.

 

 

报告人简介:臧经涛,哈尔滨工业大学讲师。臧经涛本科毕业于南开大学数学学院,在南开大学组合数学中心获得博士学位,师从陈永川院士。臧经涛的主要研究领域是组合计数,侧重于整数分拆的组合证明。主要结果发表在Adv. Math. 以及 J. Reine. Angew. Math. 等期刊上。