||1. In this talk, the speaker will talk about a new result of Kyung-Won Hwang and Younjin Kim on Alon-Babai-Suzuki's Conjecture.
2. Using two bijections, we give the most obvious $q$-analogue of the Narayana numbers based on non-crossing partitions. We also define two interesting decompositions of non-crossing partitions, and obtain recursions of joint distributions of statistics on non-crossing partitions. Using another bijection, we show that the statistic $2rs +n-bk$ on non-crossing partitions and the statistic $area$ on Dyck paths are equidistributed. Finally, we get an interesting $(q, x)$-refinement of the Catalan numbers through the connection between non-crossing partitions and $2$-Motzkin paths.