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Proofs of two conjectural Andrews-Beck type congruences due to Lin, Peng and Toh

The study on Andrews-Beck type congruences for partitions has its origin in the work by Andrews, who proved two congruences on the total number of parts in the partitions of $n$ with the Dyson rank, conjectured by George Beck. Recently, Lin, Peng andTohproved many Andrews-Beck type congruences for $k$-colored partitions. Moreover, they posed eight conjectural congruences. In this talk, we confirm two congruences modulo 11 by utilizing some $q$-series techniques and the theory of modular forms. This is a joint work with Julia Q. D. Du(Hebei Normal University).