120周年校庆系列学术活动：Combinatorics in a Truncated Board: Permutations, Lattice Paths and Combinatorial Statistics
主 讲 人 ：宋春伟 教授
地 点 ：腾讯会议：820-461-477
The studies of permutation statistics and lattice paths form a closely intertwined complex. Traditional theories are mostly about related combinatorics of a square board. In this talk, we outline extensions of traditional (des, inv) joint distributions of permutations from the domain of a square board to that of a truncated board, as well as maj q-analogue of lattice paths from an upper half board to a truncated rectangle. In either case, an isosceles triangle is cut off from the southeast corner of the board. Connections to permutations of bounded drop size are discussed in the former part. Celebrated result of F\"urlinger and Hofbauer, which is itself a refinement of the q-Catalan numbers, is generalized in the latter.
宋春伟，北京大学数学科学学院教授，现兼任中国数学会理事、组合数学与图论专业委员会委员。研究领域为Enumerative Combinatorics & Graph Theory，学术工作发表在Discrete Mathematics、Rocky Mountain J. Math.、Proceedings of the AMS等多种专业期刊，著有《组合数学》（与人合编）、《数学天书的证明》（与人合译）等。