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In a seminal 2007 paper, Andrews introduced a class of combinatorial objectsthat generalize partitions called $k$-marked Durfee symbols. Multivariate rankgenerating functions for these objects have been shown by many to haveinteresting modularity properties at certain vectors of roots of unity.Motivated by recent studies of rank generating functions for strongly unimodalsequences, we apply methods of Andrews to define an analogous class ofcombinatorial objects called $k$-marked strongly unimodal symbols thatgeneralize strongly unimodal sequences. We establish a multivariate rankgenerating function for these objects, which we study combinatorially. Weconclude by discussing potential quantum modularity properties for this rankgenerating function at certain vectors of roots of unity.

An analogue of $k$-marked Durfee symbols for strongly unimodal sequences