学 术 报 告
报告人：南开大学数学系 杜若霞 博士
题 目： Crossings and Nestings of Matchings and Partitions
Abstract: We present results on the enumeration of crossings and nestings for matchings and set partitions. Using a bijection between partitions and vacillating tableaux, we show that if we fix the sets of minimal blockelements and maximal block elements, the crossing number and thenesting number of partitions have a symmetric joint distribution. It follows that the crossing numbers and the nesting numbers distributedsymmetrically over all partitions of $[n]$, as well as over all matchings on $[2n]$. As a corollary, the number of $k$-noncrossing partitions is equal to the number of $k$-nonnesting partitions. The same is also true for matchings. An application is given to the enumeration of matchings with no $k$-crossing (or with no $k$-nesting).
地 点： 理科大楼A1414多媒体教室
时 间： 2005年4月6日（星期三）下午：3: 00—4: 00
数学系
2005-4-4
