讲座内容：

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.