Combinatorial approaches to problems about integer partitions and $q$-series

In this talk, we shall first introduce some backgrounds and definitions of partitions and mock theta functions, and then introduce some new generalizations of mock theta functions and some new results of mex-functions. This talk is based on joint works with Zhenkun Li（李振坤）, Yongshan Liu（刘勇杉）and Li Zhou（周丽）