Abstract

The study of sequences in partitions dates back at least to Sylvester. In this talk, we enumerate strict partitions with respect to the size, the number of parts, and the number of sequences of odd length. We write this generating function as a double sum $q$-series, which on one hand gives partition theoretical interpretation to the sum side of several identities obtained by Cao-Wang and Wang-Wang, on the other hand motivates us to look for further refinements of Euler's partition theorem. A close relation with the $2$-measure of partitions will also be mentioned. This is a joint work with Haijun Li.