学术报告一

报告题目：Standard Rothe Tableaux

报告人：范久瑜 副教授（四川大学）

报告时间：2020年11月7日(星期六)下午15:00-16:00

报告地点：25教18楼学术报告厅

参加人员：教师、研究生、本科生

摘要：Edelman and Greene constructed a bijection between the set of standard Young tableaux and the set of balanced Young tableaux of the same shape. Fomin, Greene, Reiner and Shimozono introduced the notion of balanced Rothe tableaux of a permutation w, and established a bijection between the set of balanced Rothe tableaux of w and the set of reduced words of w. In this talk, we introduce the notion of standard Rothe tableaux of w, which are tableaux obtained by labelling the cells of the Rothe diagram of w such that each row and each column is increasing. We show that the number of standard Rothe tableaux of w is smaller than or equal to the number of balanced Rothe tableaux of w, with equality if and only if w avoids the four patterns 2413, 2431, 3142 and 4132.

报告人简介：范久瑜，四川大学星际电子在线副教授，研究方向为代数组合，主要研究课题包括Schubert演算的组合学、对称函数、多面体的组合学等，在包括《Math. Z.》,《J. Combin. Theory, series A》，《Math. Comput.》，《J. Pure Applied Algebra》，《SIAM J. Discrete Math.》，《European J. Combin.》等期刊上发表论文十多篇。先后主持国家自然科学青年基金、面上基金等。

学术报告二

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

报告人：傅士硕 研究员（重庆大学）

报告时间：2020年11月7日(星期六)下午16:00-17:00

报告地点：25教18楼学术报告厅

参加人员：教师、研究生、本科生

摘要：In this talk, we bijectively establish recurrence relations for two triangular arrays, relying on their interpretations in terms of Schroeder paths (resp. little Schroeder paths) with given length and number of hills. The row sums of these two triangles produce the large (resp. little) Schroeder numbers. On the other hand, it is well-known that the large Schroeder 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.

报告人简介：傅士硕，博士毕业于宾夕法尼亚州州立大学，现任职重庆大学特聘研究员。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。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青年基金一项。