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报告题目： Bijective recurrences for Schröder triangles and Comtet statistics

主 讲 人：傅士硕研究员（重庆大学数学与统计学院）

报告邀请人：孙怡东教授

会议时间：2021年5月21日下午15:30-17:00

点击链接直接加入会议：

https://meeting.tencent.com/s/26oWsWX4q9mW

腾讯会议ID：574 143 622

报告摘要：

In this talk, we bijectively establish recurrence relations for two triangular arrays, relying on their interpretations in terms of Schröder paths (resp. little Schröder paths) with given length and number of hills. The row sums of these two triangles produce the large (resp. little) Schröder numbers. On the other hand, it is well-known that the large Schröder numbers also enumerate separable permutations. This propelled us to reveal the connection with a lesser-known permutation statistic, called initial ascending run (iar), whose distribution on separable permutations is shown to be given by the first triangle as well. A by-product of this result is that "iar" is equidistributed over separable permutations with "comp", the number of components of a permutation. We call such statistics Comtet and we briefly mention further work concerning Comtet statistics on various classes of pattern avoiding permutations.

个人简介：

傅士硕，2011年博士毕业于宾夕法尼亚州州立大学，2011-2012在韩国科学技术院（KAIST）做博士后研究，现任职重庆大学“百人计划”特聘研究员。研究兴趣主要为组合数学中的整数分拆理论、排列统计量同分布问题以及组合序列的伽马非负性等。已在J. Combin. Theory Ser. A, Adv. Appl. Math., SIAM Disc. Math., European J. Combin., Ramanujan J. 等杂志发表论文20余篇，多次受邀参加国际国内学术会议并作邀请报告，主持过国家自然科学基金一项。现任中国工业与应用数学学会图论组合及应用专业委员会副秘书长、中国运筹学会图论组合学分会理事。

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